A student is trying to determine the muzzle
velocity (initial) of a bullet that is too fast to
measure directly. The student fires the 0.05kg
bullet into a 4kg block of wood initially at rest.
After the collision, the block, with the bullet
embedded inside moves to the right with a
speed of 1.87m/s right.
before collision:
Pbullet
Pblock
after collision:
Pcombined
kg m/s
kg m/s
kg m/s
How fast was the bullet fired?
m/s

The titles should replace A and B are Column A should be “Time,” and Column B should be “Position.”

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It would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

1. The decay rate of a radioactive isotope is proportional to the number of radioactive atoms present in the sample at any given time.

2. The decay rate can be expressed as a function of time using the formula: R(t) = R₀ * \(e^{(-\lambda t\)), where R(t) is the decay rate at time t, R₀ is the initial decay rate, λ is the decay constant, and e is the base of the natural logarithm.

3. The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life is given as 210 days.

4. Using the half-life, we can find the decay constant (λ) using the formula: λ = ln(2) / T₁/₂, where ln(2) is the natural logarithm of 2 and T₁/₂ is the half-life.

5. Substituting the given half-life into the formula, we have: λ = ln(2) / 210.

6. Now, we need to find the time it takes for the decay rate to fall to 0.58 of its initial rate. Let's call this time "t".

7. Using the formula for the decay rate, we can write: 0.58 * R₀ = R₀ * e^(-λt).

8. Simplifying the equation, we get: 0.58 = \(e^{(-\lambda t\)).

9. Taking the natural logarithm of both sides, we have: ln(0.58) = -λt.

10. Substituting the value of λ from step 5, we get: ln(0.58) = -(ln(2) / 210) * t.

11. Solving for t, we have: t = (ln(0.58) * 210) / ln(2).

12. Evaluating the expression, we find: t ≈ 546.

13. Therefore, it would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

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Answer:

Before the parachute opens: Immediately on leaving the aircraft, the skydiver accelerates downwards due to the force of gravity. There is no air resistance acting in the upwards direction, and there is a resultant force acting downwards. The skydiver accelerates towards the ground.

Once the parachute is opened, the air resistance overwhelms the downward force of gravity. The net force and the acceleration on the falling skydiver is upward. An upward net force on a downward falling object would cause that object to slow down. The skydiver thus slows down.

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Answer:

The main focus of the nervous system is to have nerve fibers pass information throughout the body. The nervous system is crucial for keeping our bodies functioning. It is divided into two main parts, the peripheral nervous system, which are the nerves running throughout the body, and the central nervous system, which is the brain and spinal cord. The nervous system communicates signals between body parts and the brain. The nervous system keeps all body parts functioning through these signals.

Explanation:

I hope this helps!

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

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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Answer:

\( \underline{ \boxed{ yes}}\\\)

Explanation:

\(given : initial \: velocity \: (u )= 40 {ms}^{ - 1} \\ given : final \: velocity \: (u )= 0 {ms}^{ - 1} \\ given : - (acceleration) \: (a_r) = 2 {ms}^{ - 2} \\ given : distance \: (s) \: = \: ? : \\ but \: {v}^{2} = {u}^{2} + 2( a)s\\ {0}^{2} = {40}^{2} + 2( - 2)s \\ - {40}^{2} = - 4s \\ s = \frac{ - {40}^{2} }{ - 4} \\ s = \frac{1600}{4} \\s = 400 \: m\)

Answer:

ωf = 8.8 rad/s

v = 2.2 m/s

Explanation:

We will use the third equation of motion to find the maximum angular velocity of the wheel:

\(2\alpha \theta = \omega_f^2 -\omega_I^2\)

where,

α = angular acceleration = 6 rad/s²

θ = angular displacemnt = 1 rev = 2π rad

ωf = max. final angular velocity = ?

ωi = initial angular velocity = 1.5 rad/s

Therefore,

\(2(6\ rad/s^2)(2\pi\ rad)=\omega_f^2-(1.5\ rad/s)^2\\\omega_f^2=75.4\ rad/s^2+2.25\ rad/s^2\\\omega_f = \sqrt{77.65\ rad/s^2}\)

ωf = 8.8 rad/s

Now, for linear velocity:

v = rω = (0.25 m)(8.8 rad/s)

v = 2.2 m/s

To calculate the resultant force on the aircraft as it accelerates from the catapult, we can use the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy.

Since all of the kinetic energy at take-off is from the work done on the aircraft by the catapult, we can equate the work done by the catapult to the kinetic energy of the aircraft at take-off, that is:

Work done by catapult = kinetic energy of aircraft at take-off

The work done by the catapult is given by the force provided by the catapult multiplied by the distance over which it acts, that is:

Work done by catapult = force × distance

The distance over which the force provided by the catapult acts is given as 150 m, so we have:

Work done by catapult = force × 150

The kinetic energy of the aircraft at take-off is given by:

(1/2) × mass × velocity^2

Since the aircraft is initially at rest, its initial velocity is zero, so we have:

kinetic energy of aircraft at take-off = 0.5 × mass × (final velocity)^2

Using the work-energy principle, we can equate the two expressions for work done and kinetic energy, that is:

force × 150 = 0.5 × mass × (final velocity)^2

Solving for force, we get:

force = 0.5 × mass × (final velocity)^2 / 150

Therefore, the resultant force on the aircraft as it accelerates is given by:

force = 0.5 × mass × (final velocity)^2 / 150

Note that we need to know the mass and final velocity of the aircraft in order to calculate the resultant force.

The water pressure at the base is 98,000 Pa, and the force exerted at the base of the tank is 2,768,460 N.

To find the water pressure at the base of the tank, take the formula:

Pressure = density × gravity × height

In which

Density = density of water (1000 kg/m³)

Gravity = acceleration due to gravity (9.8 m/s²)

Height = height of the column

According to question:

Height of the water column = 10 m

Take the formula:

P = 1000 kg/m³ × 9.8 m/s² × 10 m

= 98,000 Pa

To find the force at the base of the tank, take the formula:

Force = Pressure × Area

In which

Pressure = pressure at the base of the tank

Area = base area of the tank

The base area of a cylindrical tank can be found by the formula:

Area = π × r²

In which:

Diameter of the tank = 6 m

To find the radius, divide the diameter by 2:

Radius = 6 m ÷ 2

= 3 m

Put the values into the formula:

Area = π × (3 m)²

= 28.27 m²

Now, find the force:

Force = 98,000 Pa × 28.27 m²

= 2,768,460 N

Thus, the water pressure at the base is 98,000 Pa, and the force exerted at the base of the tank is 2,768,460 N.

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The energy transferred in Joules by the radio when it has been switched on for 2 minutes would be 6000 Joules.

Power is defined as the rate of energy transfer or the rate at which work is done, and is given by the equation:

Power = Energy transferred / Time

Rearranging the equation to solve for energy transferred, we get:

Energy transferred = Power x Time

We are given:

Power = 50 W

Time = 2 minutes = 120 seconds

Therefore, the energy transferred by the radio when it has been switched on for 2 minutes is:

Energy transferred = Power x Time = 50 W x 120 s = 6000 J

In other words, the energy transferred by the radio is 6000 Joules.

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dnxjjc cjgnjgjnffjnfkfmgkcknsmksjs dmxmcmfkcnfjcnfjfnfjf in jfnfifnfifnf

Answer:

Electroplating is the method of depositing one metal over another in the presence of a metal salt (in aqueous solution). The water molecule is released as the final product in this process. As a consequence, electroplating is based on the theory of hydrolysis.

With a 7ms1 horizontal velocity, an object R departs from a platform XY and lands at Q. The length PQ is 0.45m if the identical object falls freely from Xy to P in 0.3 seconds.

There is no possible for the items to have the same start y-component velocity unless they're shot with distinct initial speeds given that each is launched at a various perspectives. The objects must have been shot at different speeds if they had the same maximum height.

We can observe that over the longest-range the signal reaches its maximum output value, 1, at an output data angle of 90 degrees Punts 2 are at a 90-degree angle, so is at a 45-degree angle. In other words, a projectile moves and furthest when it is fired at a 45-degree angle.

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Answer:

Gravity exist between two objects that have mass

The constant acceleration of the train is 0.33 m/s.

The average velocity can be calculated by using the formula:

velocity = distance/time

For the 1st car, the velocity is calculated as:

v₁ = 8.60 m / 1.80 s = 4.78 m / s

For the second car, velocity can be calculated as:

v₂ = 8.60 m / 1.66 s = 5.34 m / s

Now we can solve for the acceleration using the formula:

v₂² = v₁² + 2 a d

Rewriting in terms of a, we get

a = (v₂² – v₁²) / 2 d

a = (5.34)² – (4.78)² / (2 × 8.6)

a = 0.33 m/s

Therefore, the constant acceleration of the train is 0.33m/s.

what is acceleration explain?

acceleration, fee at which speed modifications with time, in terms of each pace and course. A factor or an object shifting in a directly line is improved if it hastens or slows down. motion on a circle is improved even if the velocity is steady, due to the fact the route is constantly converting

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Answer:

General Expression: E = kql/(l² + r²)^(3/2)

(a) 6.3 MN/C

(b) 22.8 MN/C

(c) 6.1 MN/C

(d) 0.63 MN/C

Explanation:

The general expression for electric field along axis of a uniformly charged ring is:

E = kqL/(L² + r²)^(3/2)

where,

E = Electric Field Strength = ?

k = Coulomb's Constant = 9 x 10⁹ N.m²/C²

q = Total Charge = 71 μC = 71 x 10⁻⁶ C

L = Distance from center on axis

r = radius of ring = 10 cm = 0.1 m

(a)

L = 1 cm = 0.01 m

Therefore,

E = (9 x 10⁹ N.m²/C²)(71 x 10⁻⁶ C)(0.01 m)/[(0.01 m)² + (0.1 m)²]^(3/2)

E = (6390 N.m³/C)/(0.00101 m³)

E =  6.3 x 10⁶ N/C = 6.3 MN/C

(b)

L = 5 cm = 0.05 m

Therefore,

E = (9 x 10⁹ N.m²/C²)(71 x 10⁻⁶ C)(0.05 m)/[(0.05 m)² + (0.1 m)²]^(3/2)

E = (31950 N.m³/C)/(0.00139 m³)

E =  22.8 x 10⁶ N/C = 27.4 MN/C

(c)

L = 30 cm = 0.3 m

Therefore,

E = (9 x 10⁹ N.m²/C²)(71 x 10⁻⁶ C)(0.3 m)/[(0.3 m)² + (0.1 m)²]^(3/2)

E = (191700 N.m³/C)/(0.03162 m³)

E =  6.1 x 10⁶ N/C = 6.1 MN/C

(d)

L = 100 cm = 1 m

Therefore,

E = (9 x 10⁹ N.m²/C²)(71 x 10⁻⁶ C)(1 m)/[(1 m)² + (0.1 m)²]^(3/2)

E = (639000 N.m³/C)/(1.015 m³)

E =  0.63 x 10⁶ N/C = 0.63 MN/C

Answer:

The decay constant, or "lambda" (λ), is the rate at which a radioactive isotope decays. It is usually measured in units of inverse time, such as seconds. In this case, the decay constant can be calculated as follows:

16:42

λ = (ln(2)/3.57 x 106) x (5.78 x 1017) = 0.

Explanation:

Answer:

Merritt Island i think

Answer:

C) The book's inertia carried it forward.

When the bus stops suddenly, the book tends to remain in motion due to its inertia. The book was at rest on the seat of the bus, and when the bus stopped suddenly, the book continued moving forward with the same speed and direction it had before the bus stopped. As a result, the book slid off the seat and onto the floor.

The angular velocity is 3.75 m/s and the centripetal force is 225 N respectively.

The angular velocity of an object with respect to some extent is a degree of the way rapid that item actions through the point's view, within the feel of the way speedy the angular function of the item modifications. An instance of angular pace is a ceiling fan. One blade will whole a complete round in a certain amount of time T, so its angular speed with respect to the middle of the ceiling fan is twoπ/T.

Calculation:-

A. angular velocity ω = v/r

                                     = 30 /8

                                      = 3.75 m/s

B. Centripetal force = mv²/r

                             = 2×30²/8

                              = 225 N

There are 3 formulations we will use to find the angular velocity. the primary comes instantly from the definition. The angular pace is the rate of alternate of the position attitude of an object with respect to time, so w = theta / t, in which w = angular pace, theta = position attitude, and t = time.

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Answer:

C₁ = 34.8 μF

C₂ = 0.2 μF

Explanation:

When the capacitors are connected in series their resultant capacitance is given by the formula:

Cs = 1/C₁ + 1/C₂

where,

Cs = Series equivalent capacitance = 4.8 μF

C₁ = Capacitance of 1st Capacitor

C₂ = Capacitance of 2nd Capacitor

Therefore,

4.8 μF = 1/C₁ + 1/C₂

(4.8 μF)(C₁ C₂) = C₁ + C₂   --------------- equation 1

When the capacitors are connected in parallel their resultant capacitance is given by the formula:

Cp = C₁ + C₂

where,

Cp = Parallel equivalent capacitance = 35 μF

Therefore,

35 μF = C₁ + C₂   -------------- equation 2

solving equation 1 and equation 2 simultaneously, we get:

C₁ = 34.8 μF

C₂ = 0.2 μF

Let's take east and west to be positive and negative, respectively, and north and south to be positive and negative, respectively. Then in terms of vectors (using ijk notation), the car first moves 200 km west,

r = (-200 km) j

then 80 km southwest,

s = (-80/√2 km) i + (-80/√2 km) j

so that its total displacement is

r + s = (-80/√2 km) i + ((-200 - 80/√2) km) j

r + s ≈ (-56.6 km) i + (-256.6 km) j

This vector has magnitude

√((-56.6 km)² + (-256.6 km)²) ≈ 262.7 km

and direction θ such that

tan(θ) = (-256.6 km) / (-56.6 km)  ==>  θ ≈ -102.4º

relative to east, or about 12.4º west of south.

Answer:

722.89

Explanation:

mass=24000kg

volume=33•2

density=?

now,

density=mass/volume

=24000/33•2

=722•89

density=722•89 kg/m^3

Answer:

1st law of motion

Explanation:

it's newton's first law of motion.

Answer:

A C E

Explanation:

Answer:The gravitational force is defined in Uniform Circular Motion and Gravitation, electric force in Electric Charge and Electric Field, magnetic force in Magnetism, and nuclear forces in Radioactivity and Nuclear Physics. On a macroscopic scale, electromagnetism and gravity are the basis for all forces.

Explanation:

Answer:

The gravitational force is defined in Uniform Circular Motion and Gravitation, electric force in Electric Charge and Electric Field, magnetic force in Magnetism, and nuclear forces in Radioactivity and Nuclear Physics. On a macroscopic scale, electromagnetism and gravity are the basis for all forces.

Answer:

In mechanics, the normal force F_n\ is the component of a contact force that is perpendicular to the surface that an object contacts, as in Figure 1

Explanation:

Answer:

Explanation:

The process can be broken down into two steps:

Heat required to raise the temperature of ice from -20°C to 0°C.

Heat required to melt ice at 0°C and raise the temperature of water from 0°C to 10°C.

Step 1:

The heat required to raise the temperature of ice can be calculated using the specific heat capacity of ice, which is 2.09 J/g°C.

Heat required = mass × specific heat capacity × change in temperature

Heat required = 10 g × 2.09 J/g°C × (0°C - (-20°C))

Heat required = 418 J

Step 2:

The heat required to melt ice and raise the temperature of water can be calculated using the heat of fusion of ice and the specific heat capacity of water.

Heat required to melt ice = mass × heat of fusion of ice

Heat required to melt ice = 10 g × 334 J/g

Heat required to melt ice = 3340 J

Heat required to raise the temperature of water can be calculated using the specific heat capacity of water, which is 4.18 J/g°C.

Heat required = mass × specific heat capacity × change in temperature

Heat required = 10 g × 4.18 J/g°C × (10°C - 0°C)

Heat required = 418 J

Total heat required = Heat required in Step 1 + Heat required to melt ice + Heat required in Step 2

Total heat required = 418 J + 3340 J + 418 J

Total heat required = 4176 J

Therefore, 4176 J of heat is required to change 10 g of ice at -20°C into water at 10°C.

We can see that the speed of the car is obtained as 12 miles per hour.

The term speed is the ratio of the distance covered to the time taken. We can see that the distance that have been covered by the boy is  24 miles. The total time that have been taken to cover this distance is 30 mins or 0.5 hours.

We now come up with the following;

Distance = 24 miles

time =  0.5 hours

We now want to compute the speed of the boy in miles per hours so we have;

Speed = 24 miles /  0.5 hours = 12 miles per hour

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The magnitude of the force P provided that the stress in the part AB is two times that of BC part is 0.8 kN.

The magnitude of the force P provided that the stress in the part AB is two times that of BC part is calculated as follows;

Take moment about the joint to determine the magnitude of the force along part BC.

120 kN x 750 mm  =  F x 1000 mm

F = ( 120 kN x 750 mm ) / ( 1000 mm )

F = 90 kN

Stress is given as force divided by area. The following equation can be used to determine the magnitude of force P.

Stress in AB = 2 times stress in BC

P/A₁  = 2F/A₂

where;

A₁ =  πd²/4  =  π(50 x 10⁻³)²/4

A₁ = 1.96 x 10⁻⁵ m²

A₂ = πd²/4  =  π(75 x 10⁻³)²/4

A₂ = 4.42 x 10⁻³ m²

P/A₁ = 2F/A₂

P = (2F x A₁) / (A₂)

P = (2 x 90 kN x 1.96 x 10⁻⁵ m² ) / ( 4.42 x 10⁻³ m² )

P = (2 x 90,000 N x 1.96 x 10⁻⁵ m² ) / ( 4.42 x 10⁻³ m² )

P = 798.2 N

P = 0.798 kN

P ≈ 0.8 kN

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Answer: 19.80 cm

Explanation:

Given

focal length \(f=6.14\ cm\)   (as focal length is positive, it is converging lens)

Image distance \(v=1.5f\)

\(v=1.5\times 6.14\\v=9.21\ cm\)

using lens formula

\(\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}\)

insert values

\(\dfrac{1}{u}=\dfrac{1}{6.14}-\dfrac{1}{8.9}\\\\\dfrac{1}{u}=0.1628-0.1123\\\\\dfrac{1}{u}=0.0505\\\\u=19.80\ cm\)

Thus, the distance of the object is 19.80 cm

Given:

Now,

The image distance will be:

→ \(v = 1.5 f\)

     \(= 1.5\times 6.14\)

     \(= 9.21 \ cm\)

By using the lens formula, we get

→ \(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\)

By putting the values, we get

→ \(\frac{1}{u} = \frac{1}{6.14} - \frac{1}{8.9}\)

   \(\frac{1}{u} = 0.1628-0.1123\)

   \(\frac{1}{u} = 0.0505\)

   \(u = 19.80 \ cm\)

Thus the answer above is correct.    

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