An electromotive force E(t) = 200, 0 ≤ t ≤ 50 0, t > 50 is applied to an LR-series circuit in which the inductance is 50 henries and the resistance is 5 ohms. Find the current i(t) if i(0) = 0.

Answers

Answer 1

Answer:

The answer is below

Explanation:

An LR series circuit has a differential equation in the form of:

\(L\frac{di}{dt}+iR=E(t)\\ \\Given\ that\ 50H,R=5\ ohms,E(t)=200,for\ 0 \leq t \leq\ 50. Hence:\\\\50\frac{di}{dt}+5i =200\\\\\frac{di}{dt}+0.1i =4\\\\Solving\ the\ differential\ equation:\\\\The\ integrating\ factor(I)=e^{\int\limits {0.1} \, dt }=e^{0.1t}. The\ DE\ becomes:\\\\e^{0.1t}\frac{di}{dt}+e^{0.1t}(0.1i) =4e^{0.1t}\\\\e^{0.1t}i=\int\limits {4e^{0.1t}} \, dt \\\\e^{0.1t}i=40e^{0.1t}+A\\\\i(t)=40+Ae^{-0.1t}\\\\but\ i(0)=0\\\\0=40+Ae^{-0.1(0)}\\\\A=-40\\\\i(t)=40-40e^{-0.1t}\\\\\)

At 50 seconds:

\(i(50)=40-40e^{-0.1*50}\\\\i(50)=40-40e^{-5}\)

\(L\frac{di}{dt}+iR=E(t)\\ \\Given\ that\ 50H,R=5\ ohms,E(t)=0,for\ t> 50. Hence:\\\\50\frac{di}{dt}+5i =0\\\\\frac{di}{dt}+0.1i =0\\\\\frac{di}{dt}=-0.1i\\\\\frac{di}{i}=-0.1dt\\\\\int\limits {\frac{di}{i}} =\int\limits {-0.1} \, dt\\ \\ln(i)=-0.1t+A\\\\taking\ exponential:\\\\i=e^{-0.1t+A}\\\\i=e^{-0.1t}e^A\\\\i(t)=Ce^{-0.1t}\\\\i(50)=40-40e^{-5}=Ce^{-5}\\\\C=40(e^5-1)\\\\i(t)=40(e^5-1)e^{-0.1t}\\\\\)

\(i(t)=\left \{ {{40-40e^{-0.1t}\ \ \ \ 0 \leq t \leq 50 } \atop {40(e^5-1)e^{-0.1t}\ \ \ \ t>50}} \right.\)


Related Questions

A low C (f = 65Hz) is sounded on a piano. If the length of the piano wire is 2.0 m and its mass density is 5.0 g/m2, determine the tension of the wire.

Answers

Answer:

338N

Explanation:

Use the formula \(f=\frac{\sqrt{\frac{T}{\frac{M}{L}} } }{2L}\)

f is the frequency, T the string tension, M the mass, and L the length

convert units to seconds, kilograms, meters

\(65Hz\ =\ \frac{\sqrt{\frac{T}{\frac{0.005kg}{m}}}}{2\cdot2m}\)

now solve for T

sqrt(T/.005) = 65*4 = 260

T = 338N

Please see the attached image

Please see the attached image

Answers

The moment of inertia of the flat square is MA²/6

What is moment of inertia?

The moment of inertia of a body is a property of the body which shows its ability to ritate about an axis.

What is the moment of inertia of the flat square?

To find the moment of inertia of the flat square through its center of mass, we know that the moment of  inertia of  a rectangular slab is given by

I = M(a² + b²)/12 where

M = mass of slab and a and b = side lengths

Now, for a flat square a = b. so,its moment of inertia is I = M(a² + b²)/12

I = M(a² + a²)/12

= 2Ma²/12

= Ma²/6

Now for the given flat square, we have that

its mass equals M and its length equals A.

So, substituting these into the equation of moment of inertia for the flat square, we have that

The moment of inertia of the flat square is given by

I = Ma²/6

I = MA²/6

So, moment of inertia is MA²/6

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1.The energy that a charge has due to its position in an electric field is called:
a. electrical kinetic energy
b. electrical potential energy.
c. electrical mechanical energy.
d. electrical potential difference.
2. For electric potential energy, we must define a reference position.
a. True
b. False
3. Charges q1 and q2 are both positive and their electric potential energy is 2 J. Then, q2 is substituted with charge q3, which is negative and has twice as much charge as q2. As a result of this substitution, the potential energy of q1 and q3:
a. -4 J
b. is 2 J.
c. -2 J
d. 4 J
4. Whenever two charges are moved toward each other, the absolute value of their potential energy:
a. stays the same.
b. increases.
c. decreases.
5. Two point charges are 10 cm apart. Charge A =+ 9 μC and charge B = - 4 μC. What is the electric potential energy between these two charges?
a. -3.24 MJ
b. -3.24 J
c. +3.24 J
d. -32.4 J
e. +32.4 J
f. -3.24 GJ
6. Two electric charges repel each other. We can be sure that which of the following could never be their electric potential energy?
A) +2 J B) -2J C) +12 J D) -12 J
a. B or D
b. A or B
c. Not enough information is given to answer
d. A or C
e. C or D
7. Electric potential:
a. is the same as electrical potential energy.
b. depends on the charge at the point where it is measured.
c. measures energy per unit charge.
d. is measured in joules.
8. A potential of 2 V means that a charge of 6 C will have a potential energy of [12 J, 6 J, 2 J, 3 J] when placed at that point.
9. A charge of +5 C is at a point in an electric field where its electric potential energy of 50 J. At that point in the field, the electric potential is
a. 250 V
b. 10 V
c. 50 V
d. Impossible to calculate without knowing the distance from the source.
e. 50 J
10. A point charge q1 is at a distance d from a point charge q2, where the electric potential is 28 V. The charge q2 is then moved to a new distance 2d away from q1. The electric potential of q1 at the new position of q2 is:
a. 56 V
b. 7 V
c. 14 V
d. 112 V
e. 28 V
11. A source charge q1 is negative and a test charge q2 is positive. Then, q2 is substituted by a negative test charge with twice the magnitude of q2. As a result of this substitution, the POTENTIAL at the position of q2 due to q1:
a. stays the same
b. decreases.
c. increases.
12 By convention, the direction of a current is taken to be the direction of motion of [positive, neutral, negative] charges. In reality, it is actually [protons, neutrons, atoms, electrons] that move in wires.
13. A charge of 15 C flows through the cross-section of a wire each minute. The current through the wire is:
a. 15 A
b. 4 A
c. 0.25 A
d. 900 A
14. A current of 3 mA flows through a wire. How much charge flows through the wire in 1 hour?
a. 3 mC
b. 1.2x10^6 C
c. 10.8 C
d. 8.3x10^-7 C
15. An ampere is a unit of electrical
a. pressure
b. charge
c. None of these
d. current
e. voltage
16. As current flows through a wire, the number of [electrons, particles, voltage, circuits] stays the same.

Answers

1. b. electrical potential energy.

2. a. True. For electric potential energy, a reference position must be defined.

3. a. -4 J. The potential energy between two charges is given by the equation U = k(q1q2)/r, where k is the electrostatic constant, q1 and q2 are the charges, and r is the separation between them. Since the potential energy is given as 2 J initially, and q2 is replaced by q3 (which is negative and twice the magnitude of q2), the potential energy becomes -4 J.

4. c. decreases. The potential energy between two charges decreases as they are moved closer together.

5. b. -3.24 J. The electric potential energy between two point charges is given by the equation U = k(q1q2)/r, where k is the electrostatic constant, q1 and q2 are the charges, and r is the separation between them. Substituting the values into the equation, we get U = (9x10^(-6) C)(-4x10^(-6) C)/(0.1 m) = -3.24 J.

6. a. B or D. Electric potential energy can never be negative if the charges repel each other.

7. c. measures energy per unit charge.

8. 12 J. The potential energy is given by the equation U = qV, where U is the potential energy, q is the charge, and V is the potential. Substituting the values into the equation, we get U = (6 C)(2 V) = 12 J.

9. b. 10 V. The electric potential is given by the equation V = U/q, where V is the potential, U is the potential energy, and q is the charge. Substituting the values into the equation, we get V = 50 J/5 C = 10 V.

10. c. 14 V. The electric potential is inversely proportional to the distance from a point charge. When the distance is doubled, the potential is halved. Therefore, the electric potential at the new position of q2 is 28 V/2 = 14 V.

11. c. increases. The potential at the position of q2 due to q1 increases when a negative test charge is substituted with twice the magnitude of the positive test charge.

12. By convention, the direction of a current is taken to be the direction of motion of negative charges. In reality, it is actually electrons that move in wires.

13. c. 0.25 A. The current is defined as the rate of flow of charge. Given that 15 C flows through the wire each minute, the current is 15 C/60 s = 0.25 A.

14. b. 1.2x10^6 C. The charge flowing through the wire is given by the equation Q = It, where Q is the charge, I is the current, and t is the time. Substituting the values into the equation, we get Q = (3x10^(-3) A)(1 hour)(3600 s/hour) = 1.2x10^6 C.

15. d. current. An ampere is a unit of electric current.

16. electrons. As current flows through a wire, it is actually electrons that move. The flow of electrons constitutes the electric current.

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Particle A has less mass than particle B. Both are pushed forward across a frictionless surface by equal forces for 1 s. Both start from rest. Which is true? A. A has more momentum. B. B has more momentum. C. A and B have the same momentum D. Not enough information.

Answers

Answer:

Both will have the same momentum.

P = M v     momentum

v = a t   for uniform acceleration

P = M a t

But a = F / M

P = M (F / M) t = F t    so both have the same momentum

Type the correct answer in the box. Spell all words correctly.
Mention the term
refers to having a generalized (and biased) belief about a particular group of people.

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In social psychology, a stereotype is a generalized belief about a particular category of people.

What is stereotype ?

A stereotype can be described as the accepted, condensed, and essentialist opinion  with regards to certain population.

I should be nted hat his can be related to  gender identity, race  as well as ethnicity, country,  however there are other things that an be used frequently used to stereotype groups. Stereotypes are pervasively present in both the larger social structure and culture.

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PLEASE ANSWER FASG I WILL MARK BRAINELIST PLEASEEEEE
The number of protons in the nucleus of an atom determines the species of the atom, i.e., the element to which the atom belongs. An atom has the same number of protons and neutrons. But the electron number cannot be used instead because (5 points)
a. electrons are not within the nucleus
b. electrons are negatively charged
c. electrons can be removed from or added to an atom
d. electrons are lighter than protons

Answers

The electron number cannot be used instead because electrons can be removed from or added to an atom (option C)

Why the electron number cannot be used instead?

The element of an atom is determined by its proton count, while the electron count can exhibit variability. Take, for instance, a sodium atom, which encompasses 11 protons and 11 electrons. However, it has the capacity to relinquish one electron, transforming into a sodium ion housing only 10 electrons.

This occurs due to the relatively loose binding of electrons to the nucleus, enabling their removal through the influence of an electric field or alternative mechanisms.

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A 2800-lbm car climbs a 1160 ft. long uphill road which is inclined at 15o (to the horizontal) and covers the distance in 12 sec. Determine the power required if the car covers the distance (a) at constant velocity, (b) from an initial velocity, at the bottom of the hill, of 10 mph to a final velocity of 50 mph at the top of the hill and (c) from an initial velocity of 45 mph to a final velocity of 15 mph. Neglect the effects of friction and wind resistance.

Answers

Answer:

a) P = 70054.3 W,  b)  P = 18820 W,  c)   P = 14116.7 W

Explanation:

Power is defined as work per unit of time

         P = W / t = F x / t

         P = F v

a) in this case the velocity is constant, let's use the equilibrium relation to find the force.

Let's set a reference system with the x axis parallel to the plane

           

        F - Wₓ = 0

         F = Wₓ

with trigonometry let's decompose the weight

        sin θ = Wₓ / W

        Wₓ = W sin θ

         

          F = W sin 15

          F = 2800 sin 15

          F = 724.7 lb

we look for the speed, as it rises with constant speed we can use the relations of uniform motion

          v = x / t

          v = 1160/12

          v = 96.67 ft / s

we calculate the power

          P = 724.7 96.67

          P = 70054.3 W

b) In this case, the speed of the vehicle changes during the ascent, so we use the relationship between work and the change in kinetic energy

           W = ΔK

           W = ½ m v_f² - ½ m v₀²

   let's reduce to the SI system

           v₀ = 10 mph (5280 ft / 1 mile) (1h / 3600 s = 14.67 ft / s

           v_f = 50 mph (5280 ft / 1 mile) (1 h / 3600s) = 73.33 ft.s

           

 mass :         m = w / g

           W = ½ 2800/32 (73.33² - 14.67²)

           W = 225841 J

we calculate the average power

           P = W / t

           P = 225841/12

           P = 18820 W

c) we repeat the previous procedure

          v₀ = 45 mph = 66 ft / s

          v_f = 15 mph = 22 ft / s

          W = ½ 2800/32 (22² - 66²)

          W = -169400 J

         

          P = W / t

          P = 169400/12

          P = 14116.7 W

PLEASE HELP ON QUESTION ASAP. if answer is correct i will rate you five stars a thanks and maybe even brainliest.
Alex drove for 3 hours at average speed of 60mph and for 2 hrs at 45 miles per hour. Whats his average speed for the whole journey.

also could you please show me how our working out should look like in an exam

Answers

The average speed of the whole journey is 54 mph.

To find the average speed of the entire journey, you will need to use the formula, Average speed = Total distance ÷ Total time. So, in this case, the total distance is the sum of the distances traveled at 60 mph and 45 mph, and the total time is the sum of the times taken to cover these distances. Let's calculate:Distance covered at 60 mph = 60 mph × 3 hours = 180 milesDistance covered at 45 mph = 45 mph × 2 hours = 90 milesTotal distance covered = 180 miles + 90 miles = 270 milesTotal time taken = 3 hours + 2 hours = 5 hoursTherefore, the average speed for the whole journey will be:Average speed = Total distance ÷ Total time= 270 miles ÷ 5 hours= 54 miles per hourSo, the average speed of the whole journey is 54 mph.In an exam, it is important to show all the necessary steps and calculations, as demonstrated above. It is also essential to label the units clearly, and write down the formula used. Lastly, a summary statement or answer to the question should be provided.

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The magnetic field B at all points within the colored circle of the figure (Figure 1) has an initial magnitude of 0.780 T. (The circle could represent approximately the space inside a long, thin solenoid.) The magnetic field is directed into the plane of the diagram and is decreasing at the rate of 0.0300 T/s.
a) What is the magnitude of the induced electric field at any point on the circular conducting ring with radius r = 0.100 m ?
b) What is the direction of this field at any point on the circular conducting ring?
c) What is the current in the ring if its resistance is 4.00 Ω ?
d) What is the emf between points a and b on the ring?
e) If the ring is cut at some point and the ends are separated slightly, what will be the emf between the ends?

The magnetic field B at all points within the colored circle of the figure (Figure 1) has an initial

Answers

The magnitude of the induced electrical field is 0.0015V/m, the field is pointing towards the clockwise direction while the current in the ring will be 0.0002355A if the resistance is 4 ohms. The emf between point a and b is zero and the EMF across the point if they're slightly separated between the ends is 0.000942V

To solve this question, we would have to go about each one individually

Data:

\(r=10cm=0.1m\\\)

a.

The magnitude of the induced electrical field at any point within the radius is

\(\int\limits^a_b {E} \, du=\frac{dU}{dt}=\pi \frac{dB}{dt}=\pi r^{2}\frac{dB}{dt}\\E*2\pi r=\pi r^{2}\frac{dB}{dt} \\E=\frac{r}{2}\frac{dB}{dt}=\frac{0.1}{2}*0.03=0.0015V/m\)

b.

The field is pointing towards the clockwise direction.

c.

The current in the ring if we are given a resistance of 4ohms

\(I=\frac{emf}{R}=\frac{\pi r^{2}\frac{dB}{dt} }{R} =\frac{\pi (0.1)^2*0.03}{4} =0.0002355A\)

d.

The emf between point a and b is zero

e.

The EMF across two points if they're separated by small distance across the ring is

we would use the formula to solve for the EMF

\(E=\pi r^{2}\frac{dB}{dt}=\pi (0.1)^2*0.03=0.000942V\)

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what are the factors affecting center of mass in an object

Answers

- The position of mass from the axis.
- The axis of the system.
- The distribution of mass.
- The mass of the rigid body.

A 50.0 kg driver is riding at 35.0 m/s in her red sports car when she must suddenly slam on the brakes to avoid
hitting a deer crossing the road. She strikes the air bag, which brings her body to a stop in 0.500 s.
What average force does the seat belt exert on her?

A 50.0 kg driver is riding at 35.0 m/s in her red sports car when she must suddenly slam on the brakes

Answers

Answer:

3500N

Explanation:

Given parameters:

Mass of driver  = 50kg

Speed  = 35m/s

Time  = 0.5s

Unknown:

Average force the seat belt exerts on her = ?

Solution:

The average force the seat belt exerts on her can be deduced from Newton's second law of motion.

   F = mass x acceleration

So;

     F  = mass x  \(\frac{change in velocity }{time}\)

  F  = 50 x \(\frac{35}{0.5}\)    = 3500N

A 0.0400 kg meter stick is placed on a thin rod at the 30.0 cm mark. What is the minimum mass required to be placed on the 0.00 cm mark on the stick to maintain equilibrium?

Answer in kg

Answers

The minimum mass required to be placed on the 0.00 cm mark of the meter stick to maintain equilibrium is 0.120 kg.

To maintain equilibrium, the torques acting on the meter stick must balance each other. The torque is given by the formula:

τ = r * F * sin(θ)

where τ is the torque, r is the distance from the pivot point to the point where the force is applied, F is the force applied, and θ is the angle between the force vector and the lever arm.

In this case, the meter stick is in equilibrium when the torques on both sides of the pivot point cancel each other out. The torque due to the weight of the meter stick itself is acting at the center of mass of the meter stick, which is at the 50.0 cm mark.

Let's denote the mass to be placed on the 0.00 cm mark as M. The torque due to the weight of M can be calculated as:

τ_M = r_M * F_M * sin(θ)

where r_M is the distance from the pivot point to the 0.00 cm mark (which is 30.0 cm), F_M is the weight of M, and θ is the angle between the weight vector and the lever arm.

Since the system is in equilibrium, the torques on both sides of the pivot point must be equal:

τ_M = τ_stick

r_M * F_M * sin(θ) = r_stick * F_stick * sin(θ)

Substituting the given values:

30.0 cm * F_M = 20.0 cm * (0.0400 kg * 9.8 m/s^2)

Solving for F_M:

F_M = (20.0 cm / 30.0 cm) * (0.0400 kg * 9.8 m/s^2)

F_M = 0.0264 kg * 9.8 m/s^2

F_M = 0.25872 N

Finally, we can convert the force into mass using the formula:

F = m * g

0.25872 N = M * 9.8 m/s^2

M = 0.0264 kg

Therefore, the minimum mass required to be placed on the 0.00 cm mark of the meter stick to maintain equilibrium is 0.120 kg.

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vector A has a magnitude of 8unit Victor has a magnitude of 80 units and makes angle of 45° with the Positive x-axis Vector B has the same magnitude of 8 unit anddirected a long the negative x-axis alon find the magnitude and direction of A+B. ​

Answers

Part: a

First let's represent each vector on a grid.

When we combine vectors visually, we connect the tip (arrow side) of one vector to the tail (non-arrow side) of the other. The vector is then drawn from the beginning point to the final position.The graphical representation of the sum of vectors \($\vec{A}$\)and \($\vec{B}$\) is:[See attachment]

Part: b

The graphical representation \($\vec{A}-\vec{B}$\) is:  [See attachment]

What is Vectors?

Vectors are things that have a magnitude as well as a direction. They may be represented numerically by a number expressing the magnitude and an angle representing the magnitude. They can also be represented visually, with addition and subtraction.A vector is a number that defines not only the size of an object but also its movement or location with respect to another point or object. It is sometimes referred to as a Euclidean vector, a geometric vector, or a spatial vector.The length of the segment of the directed line is known as the magnitude of a vector in mathematics, and the angle at which the vector is slanted displays the vector's direction.

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vector A has a magnitude of 8unit Victor has a magnitude of 80 units and makes angle of 45 with the Positive
vector A has a magnitude of 8unit Victor has a magnitude of 80 units and makes angle of 45 with the Positive
vector A has a magnitude of 8unit Victor has a magnitude of 80 units and makes angle of 45 with the Positive

An airplane flies 200 km due west from city A to city B and then 325 km in the direction of 29.5° north of west from city B to city C.(a) In straight-line distance, how far is city C from city A?_____ km(b) Relative to city A, in what direction is city C?_____ ° north of west

Answers

We are given the following situation:

Part (a) we are asked to determine the distance from C to A. To do that we will use the cosine law, which is the following:

\(a^2=b^2+c^2-2bc\cos A\)

Where angle "A" is the angle opposite to side "a". In the given case, we have that:

\(\begin{gathered} a=D_{CA} \\ b=325k\text{m } \\ c=200km \\ A=x \end{gathered}\)

We can determine angle "x" using the fact that it is supplementary to the 29.5° angle, therefore, the add up to 180°:

\(29.5+x=180\)

Subtracting 29.5 from both sides we get:

\(\begin{gathered} x=180-29.5 \\ x=150.5 \end{gathered}\)

Now we substitute the values:

\(D_{CA}^2=325^2+200^2-2(325)(200)\cos150.5\)

We take the square root to both sides:

\(D_{CA}=\sqrt{325^2+200^2-2(325)(200)\cos150.5}\)

Solving the operations we get:

\(D_{CA}=508.7\)

Therefore, the distance from city C to city A is 508.7 km.

Part (b) We are asked to determine angle "y". To do that we will use the sine law:

\(\frac{\sin A}{a}=\frac{\sin B}{b}\)

Where "A" is the angle opposite to side "a" and "B" is the angle opposite to side "b".

Now, we substitute the values:

\(\frac{\sin150.5}{508.7}=\frac{\sin y}{325}\)

Now, we solve for "y". First, we multiply both sides by 325:

\((325)(\frac{\sin(150.5)}{508.7})=\sin y\)

Now, we take the inverse function of the sine:

\(\sin^{-1}((325)(\frac{\sin(150.5)}{508.7}))=y\)

Solving the operations we get:

\(18.34=y\)

Therefore, the direction is 18.34° North of the west.

An airplane flies 200 km due west from city A to city B and then 325 km in the direction of 29.5 north

Ellie has a more complicated relationship with her body. She often experiences a gender identity that doesn’t align with her body. What might this way of feeling be linked to?
A. Misinformation
B. Gender Dysmorphia
C. Construed body image
D. Positive body image

Answers

Ellie's experience of a gender identity that doesn't align with her body is likely linked to gender dysphoria, a condition characterized by distress caused by the incongruence between one's internal sense of gender and assigned sex at birth.

The correct answer is option B.

Gender dysphoria refers to the distress or discomfort individuals may experience when their gender identity does not match the sex they were assigned at birth. It involves a deep-rooted sense of incongruence between one's internal sense of gender and the external physical characteristics.

It is important to note that gender dysphoria is not a result of misinformation or a lack of understanding. It is a genuine psychological condition recognized by medical and mental health professionals. Individuals with gender dysphoria often experience significant distress and may seek gender-affirming interventions, such as hormone therapy or gender-affirming surgeries, to align their physical appearance with their gender identity.

Misinformation, on the other hand, refers to inaccurate or misleading information, which may not directly relate to Ellie's experience. Construed body image and positive body image are also not directly linked to Ellie's situation. Construed body image refers to the way individuals perceive their own bodies, which may be influenced by various factors, while positive body image refers to a healthy and accepting attitude toward one's own body.

In summary, Ellie's experience of a gender identity that doesn't align with her body is likely linked to gender dysphoria. Gender dysphoria involves distress or discomfort resulting from a mismatch between an individual's internal sense of gender and their assigned sex at birth.

Therefore, among the options provided the correct answer is option B.

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what is the coefficient of static friction of wood on wood surfaces?

Answers

We know that the coefficient of static friction of wood on wood surfaces is normally found between 0.25 and 0.55.

QUESTION 3 (Start on a new page.)
A small disc, C, is thrown vertically upwards at a speed of 15 m-s¹ from the edge of
the roof of a building of height 30 m. AFTER 0,5 s, a small ball B is shot vertically
upwards from the foot of the building at a speed of 40 m-s in order to hit disc C.
Ignore the effects of air resistance.
3.1
3.2
3.3
15 m-s¹
30 m
Explain the term projectile.
Calculate the:
40 m-s¹
B
3.2.1
Time taken by disc C to reach its maximum height
3.2.2
Maximum height above the ground reached by disc C
Calculate the time from the moment that disc C was thrown upwards until
the time ball B hits the disc..
(2)
(3)
(4)
(6)

Answers

A projectile is an object thrown into the air and subject only to gravity and, if applicable, air resistance. The time taken by disc C to reach its maximum height is approximately 1.53 seconds, and its maximum height above the ground is around 11.48 meters. The time from when disc C was thrown upwards until ball B hits the disc is roughly 1.29 seconds.

3.1 Explanation of the term projectile:

A projectile refers to an object that is launched or thrown into the air and is subject only to the forces of gravity and air resistance (if applicable). The motion of a projectile can be analyzed independently of its mass, shape, or any other physical property. The key characteristic of a projectile is that it follows a curved path known as a trajectory.

When a projectile is launched, it moves along a parabolic trajectory due to the combination of its initial velocity and the force of gravity acting vertically downward. The horizontal motion of a projectile remains constant and unaffected by gravity, while the vertical motion is influenced by the acceleration due to gravity.

The path of a projectile can be described mathematically by considering its initial velocity, angle of projection, and the acceleration due to gravity. Projectile motion finds applications in various fields, such as sports, engineering, and physics, where objects are launched or thrown.

3.2.1 Time taken by disc C to reach its maximum height:

To determine the time taken by disc C to reach its maximum height, we can use the kinematic equation for vertical motion. The equation is:

vf = vi + at

Where:

vf = final velocity (which is zero at the maximum height)

vi = initial velocity

a = acceleration (in this case, acceleration due to gravity, -9.8 m/s²)

t = time

Since the disc is thrown vertically upwards, its initial velocity is 15 m/s. We want to find the time it takes for the disc to reach its maximum height, so we'll use the equation and solve for time (t):

0 = 15 + (-9.8)t

Rearranging the equation, we get:

9.8t = 15

t = 15 / 9.8

Calculating this, we find:

t ≈ 1.53 seconds

Therefore, it takes approximately 1.53 seconds for disc C to reach its maximum height.

3.2.2 Maximum height above the ground reached by disc C:

To determine the maximum height reached by disc C, we can use another kinematic equation for vertical motion:

vf² = vi² + 2ad

Where:

vf = final velocity (which is zero at the maximum height)

vi = initial velocity

a = acceleration (in this case, acceleration due to gravity, -9.8 m/s²)

d = displacement (maximum height)

Since we know the initial velocity (vi) and acceleration (a), we can solve for the displacement (d), which represents the maximum height:

0² = 15² + 2(-9.8)d

Rearranging the equation, we get:

0 = 225 - 19.6d

19.6d = 225

d = 225 / 19.6

Calculating this, we find:

d ≈ 11.48 meters

Therefore, the disc C reaches a maximum height of approximately 11.48 meters above the ground.

Calculating the time from the moment that disc C was thrown upwards until the time ball B hits the disc:

To find the time it takes for ball B to hit disc C, we need to calculate the time it takes for both objects to reach the same height.

Since disc C was thrown upwards from the edge of the roof and ball B was shot vertically upwards from the foot of the building, we need to consider the additional height of the building (30 meters).

The time it takes for disc C to reach the ground is the same as the time it takes for ball B to reach a height of 30 meters above the ground.

Using the kinematic equation for vertical motion, we can calculate the time for ball B:

d = vit + 0.5at²

Where:

d = displacement (30 meters)

vi = initial velocity (40 m/s)

a = acceleration (acceleration due to gravity, -9.8 m/s²)

t = time

30 = 40t + 0.5(-9.8)t²

Rearranging the equation, we get:

4.9t² + 40t - 30 = 0

Solving this quadratic equation, we find:

t ≈ 1.29 seconds or t ≈ -5.82 seconds

Since time cannot be negative in this context, we discard the negative solution.

Therefore, it takes approximately 1.29 seconds from the moment that disc C was thrown upwards until ball B hits the disc.

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With a 9.0 voltage battery connected with two resistors, one is 10 ohms and the other resistor is at 20 ohms, what is the voltage drop across the battery?

A) -1.00v
B) -3.00v
C) -9.00v
D) -12.00v

Answers

With a 9.0 voltage battery connected with two resistors, one is 10 ohms and the other resistor is at 20 ohms the voltage drop across the battery 1 volt. Thus, option A is correct.

What will be the voltage supplied?

Given data

voltage supplied Vs= 1.5 volts

resistance R1= 1000 ohms

resistance R2= 500 ohms

The total resistance is

Rt= 1000+ 500

Rt= 1500 ohms

In series connection the current is the same for all components while the voltage divides across all components,the voltages consumed by each individual resistance is equal to the source voltage.

Therefore, With a 9.0 voltage battery connected with two resistors, one is 10 ohms and the other resistor is at 20 ohms the voltage drop across the battery 1 volt. Thus, option A is correct.

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In a DC generator, the generated emf is directly proportional to the

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In a DC generator, the generated electromotive force (emf) is directly proportional to the rotational speed of the generator's armature and the strength of the magnetic field within the generator.

This relationship is described by the equation for the generated emf in a DC generator:

Emf = Φ * N * A * Z / 60

Where:

Emf is the generated electromotive force (in volts),

Φ is the magnetic flux density (in Weber/meter^2\(meter^2\) or Tesla),

N is the number of turns in the armature winding,

A is the effective area of the armature coil (in square meters),

Z is the total number of armature conductors, and

60 is a constant representing the conversion from seconds to minutes.

From this equation, we can see that the generated emf is directly proportional to the magnetic flux density (Φ) and the product of the number of turns (N), effective area (A), and the total number of armature conductors (Z). This means that increasing any of these factors will result in a higher generated emf.

The magnetic flux density (Φ) can be increased by using stronger permanent magnets or increasing the strength of the field windings in the generator.

The number of turns (N) and the effective area (A) are design parameters and can be optimized for a specific generator. Increasing the number of turns or the effective area will result in a higher generated emf.

Similarly, the total number of armature conductors (Z) can be increased to enhance the generated emf.

By controlling and optimizing these factors, the generated emf in a DC generator can be increased, resulting in higher electrical output. However, it is important to note that there are practical limits to these factors based on the design and construction of the generator.

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PLE.ASE HURRY DUE IN 20 MINWhat is the independent variable (the variable that was changed ) in this investigation? How was it measured? Include the units in your answer.
Answer:

What was the dependent variable (the variable that changed because of the independent variable) in this investigation? How was it measured? Include the units in your answer. The variables Car 1 3.64 3.54 3.69 Car 2 3.24 3.47 3.36 Meters Each car traveled 2.5

Answers

Answer:

Do you want the independent or dependent? Independent is the Car and the dependent is the meters traveled.

Explanation:

Answer:

sample answer

In this situation, elevation is dependent on time. So, the dependent variable is elevation in feet.

Explanation:

Ball 1, with a mass of 110 g and traveling at 15 m/s, collides head on with ball 2, which has a mass of 340g and is initially at rest.

What is the final velocity of the ball 2 if the collision is perfectly elastic?

What is the final velocity of the ball 2 if the collision is perfectly elastic?

What is the final velocity of the ball 1 if the collision is perfectly inelastic?

What is the final velocity of the ball 2 if the collision is perfectly inelastic?

Answers

The final velocity of the ball 2 if the collision is perfectly elastic is 5.87 m/s.

The final velocity of the ball 2 if the collision is perfectly elastic  7.12 m/s.

The final velocity of the ball 1 if the collision is perfectly inelastic 4.4 m/s

The final velocity of the ball 2 if the collision is perfectly inelastic 4.4 m/s

Momentum is defined as product of mass and velocity of the body. It is denoted by letter p and it is expressed in kg.m/s. Mathematically p = mv. it discuss the moment of the body. body having zero mass or velocity has zero momentum. The dimensions of the momentum is [M¹ L¹ T⁻¹].

according to conservation law of momentum,

momentum before collision is equal to momentum after collision.

for elastic collision,

m₁v₁ +m₂v₂ = m₁v₁' + m₂v₂'

for inelastic collision,

m₁v₁ +m₂v₂ = (m₁+ m₂)v

where,

mass of the ball 1 m₁ = 110g = 0.11 kg

mass of the ball 2 m₂ = 340 g = 0.34kg

initial velocity of ball 1 v₁ = 15 m/s

initial velocity of ball 2 v₂ = 0 m/s

final velocity of ball 1 v₁' = ?

final velocity of ball 2 v₂' = ?

velocity of both ball v = ?

for elastic collision,

m₁v₁ +m₂v₂ = m₁v₁' + m₂v₂'

putting all the values,

0.11× 15 = 0.11v₁' + 0.34v₂'

1.65 = 0.11v₁' + 0.34v₂' _______1)

According to conservation energy in elastic collision,

1/2m₁v₁² + 1/2m₂v₂² = 1/2m₁v₁'² + 1/2m₂v₂'²

1/2×0.11×15² = 1/2×0.11×v₁'² + 1/2×0.34×v₂'²

12.37 = 0.055×v₁'² + 0.17×v₂'²______2)

Solving this simultaneous equation we get,

v₁' = 5.87 m/s

v₂'= 7.12 m/s

for inelastic collision,

m₁v₁ +m₂v₂ = (m₁+ m₂)v

0.11×18 + 0 = (0.11 + 0.34 )v

v = 4.4 m/s

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4. With respect to a mass of 1kg. (a) How much change in elevation must it undergo to change its potential energy by 1 kJ? (g=9.8 ms²) ​

Answers

Answer:

102 m upwards.

Explanation:

Just from a qualitative analysis we can tell the mass it needs to go upwards. How much we determine with the fact that the increase will be - in absolute value - equal to the work gravity does on it to go down that same distance.

Fixed that work being 1 kJ, we get

\(\vec F \cdot \vec{ \Delta h} = |F| |\Delta h| cos 0 = ( 9.8 N )\Delta h \cdot 1 = 10^3 J\\\Delta h = \frac {10^3}{9,8} m \approx 102 m\)

A runner sprints for 20 minutes at an average pace at 7mph.what is the distance traveled?

Answers

Answer:

A runner sprints for 20 minutes at an average pace at 7mph.what is the distance traveled?

Explanation:

140

A 400 kg bomb sitting at rest on a table explodes into three pieces. A 150 kg piece moves off to the East with a velocity of 150 m/s. A 100 kg piece moves off with a velocity of 200 m/s at a direction of south 60° West.
What is the velocity of the third piece?

Answers

The velocity of the third piece is (81.25 m/s, -43.3 m/s).

To determine the velocity of the third piece, we can use the principle of conservation of momentum.

Given:

Mass of the first piece (m1) = 150 kg

Velocity of the first piece (v1) = 150 m/s (to the East)

Mass of the second piece (m2) = 100 kg

Velocity of the second piece (v2) = 200 m/s at a direction of south 60° West

Let's break down the velocities into their respective horizontal (x) and vertical (y) components.

For the first piece:

v1x = 150 m/s (since it's moving to the East)

v1y = 0 m/s (no vertical component)

For the second piece:

v2x = 200 m/s * cos(60°) = 200 m/s * 0.5 = 100 m/s (horizontal component)

v2y = -200 m/s * sin(60°) = -200 m/s * 0.866 = -173.2 m/s (vertical component, negative since it's moving downward)

Now, let's calculate the momentum of the first and second pieces:

The momentum of the first piece (p1) = m1 * v1

= 150 kg * 150 m/s

= 22,500 kg·m/s

The momentum of the second piece (p2) = m2 * v2

= 100 kg * (100 m/s, -173.2 m/s)

= (10,000 kg·m/s, -17,320 kg·m/s)

To find the total momentum after the explosion, we can add the momenta of the individual pieces:

Total momentum after the explosion = p1 + p2

= (22,500 kg·m/s, 0 kg·m/s) + (10,000 kg·m/s, -17,320 kg·m/s)

= (32,500 kg·m/s, -17,320 kg·m/s)

The total momentum after the explosion should also be equal to the momentum of the third piece:

The momentum of the third piece (p3) = m3 * v3

Given:

Mass of the third piece (m3) = 400 kg (calculated from the given mass of the bomb)

Let's assume the velocity of the third piece is (v3x, v3y).

Therefore, we have the equation:

(32,500 kg·m/s, -17,320 kg·m/s) = 400 kg * (v3x, v3y)

By equating the x and y components separately, we can solve for the velocity components of the third piece:

32,500 kg·m/s = 400 kg * v3x

-17,320 kg·m/s = 400 kg * v3y

Solving these equations, we find:

v3x = 81.25 m/s

v3y = -43.3 m/s

Therefore, the velocity of the third piece is approximately (81.25 m/s, -43.3 m/s).

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Question 15 of 25
A horticulturist is planning a garden that is 1 mx 3 m. She uses a model to
plan it. Which dimensions could she use to make a scale model?
O A. 0.5 mx 1.5 m
O B. 50 cm x 100 cm
O C. 1 mx 2 m
D. 16 cm x 36 cm
SUBMIT

Answers

Answer:

0.5 m x 1.5 m

What 2 factors do you need in order to calculate speed?

Answers

Answer:

Distance and time.

Explanation:

Speed=Distance/time

The two factors which we need in order to calculate the speed of an object are the distance covered by the object and the time taken to cover that distance.

What is Speed?

Speed is the rate of change of position of an object in any direction. Speed is a scalar quantity as it has only magnitude and no direction. It is measured as the ratio of the distance covered by an object to the time taken in which the distance was covered by that object.

Speed has the dimension of distance covered by the time taken. Thus, the SI unit of speed is the combination of the basic units of distance and the basic unit of Time. Thus, the SI unit of speed is meter per second (m/s).

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In 1656, the Burgmeister (mayor) of the town of Magdeburg, Germany, Otto Von Guericke, carried out a dramatic demonstration of the effect resulting from evacuating air from a container. It is the basis for this problem. Two steel hemispheres of radius 0.430 m (1.41 feet) with a rubber seal in between are placed together and air pumped out so that the pressure inside is 15.00 millibar. The atmospheric pressure outside is 940 millibar.
1. Calculate the force required to pull the two hemispheres apart. [Note: 1 millibar=100 N/m2. One atmosphere is 1013 millibar = 1.013×105 N/m2 ]
2. Two equal teams of horses, are attached to the hemispheres to pull it apart. If each horse can pull with a force of 1450N (i.e., about 326 lbs), what is the minimum number of horses required?

Answers

The force required to pull the two hemispheres is 46622.72N

Calculation and Parameters

( Note: 1 millibar=100 N/m2. One atmosphere is 1013 millibar = 1.013×105 N/m2 ]

The contact area between the hemispheres is (pi x 0.400^2) = 0.5024m^2.

Pressure difference = (940 - 12)

= 928 millibars.

(928 x 100)

= 92,800N/m^2.

Therefore, the required force to pull the two hemispheres is

(92800 x 0.5024)

= 46622.72N.

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PLS HELP WILL GIVE BRAINLIST
what is the rate at which an object moves towards a target in

A speed B Arc C force D trajectory

Answers

Answer: The rate at which an object moves towards a target is Speed

Explanation:

Rate is something that tells us amount of solmething that changes in one unit of time.

Speed is defined as the measure of the rate of movement of a body expressed either as the distance travelled divided by the time taken.

Arc is defined as the apparent path described above and below the horizon taken up by a celestial body.

Force is defined as a push or pull upon an object resulting from the object's interaction with another object.

Trajectory is defined as the path followed by an object moving under the action of given force.

What is the relation between height and energy?

Answers

Since the gravitational potential energy of an object is directly proportional to its height above the zero position, a doubling of the height will result in a doubling of the gravitational potential energy. A tripling of the height will result in a tripling of the gravitational potential energy.

A negatively charged particle is travelling in a magnetic field. This is represented in
Fig. 9.1. The direction of the magnetic field is into the page.

 A negatively charged particle is travelling in a magnetic field. This is represented inFig. 9.1. The

Answers

The right hand rule allows to find the result for the direction of the magnetic force is:

In the attachment we see the direction of the force. The force is parallel to the page pointing to the right.

Magnetic force.

The magnetic force is given by the cross product of the velocity of the particle by the magnetic field, by the cross product the three vectors are perpendicular.

             F= q v x B

Where bold indicates vectors, F is force, q is charge, v is velocity, and B is magnetic field.

The right hand rule.

The direction of the force can be obtained from the right hand rule, for a positive particle:

The thumb points in the direction of the speed. Extended fingers point in the direction of the magnetic field. The palm of the hand is in the direction of the force.  In the case of a negative charge the force direction is opposite.

In the attachment we see a diagram of these vectors, using the right-hand rule:

The thumb is in the direction of the particle speed.

The extended fingers are entered into the page that is the difference of magnetic field.

The palm of the hand, which is the direction of the force, is in the plane of the page and because it is negatively charged, it points to the right.

In conclusion using the right hand rule we can find the result for the direction of the magnetic force is:

In the attachment we see the direction of the force. The force is parallel to the page to the right.

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 A negatively charged particle is travelling in a magnetic field. This is represented inFig. 9.1. The
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