Select the correct answer.
What are the directions of an object's velocity and acceleration vectors when the object moves in a circular path with a constant speed?
OA. The question is meanimgless, since the acceleration is zero.
ов.
The vectors point in opposite directions.
Oc.
Both vectors point in the same direction.
OD
The vectors are perpendicular,
Answer:
A
Explanation:
If the object is moving at a constant speed, the object isn't accelerating as the velocity doesn't change.
Answer: C.
Explanation: plato users
A mobile at the art museum has a 2.0 kg steel cat and a 4.0 kg dog suspended from a lightweight cable as shown in the figure below. It is found that θ1=20∘ when the center rope is adjusted to be perfectly horizontal. What are the tension and the angle of the rope 3?
The equilibrium condition allows finding the result for the tension in cable 3 of the system is:
T₃ = 66.7 N
Given parameters
Cat mass mc = 2.0 kg Mass of the dog md = 4.0 kg Angles θ₁ = 20ºTo find
Tension cable 3
Newton's second law gives the relationship between the force, the mass and the acceleration of the bodies, in the spatial case that the acceleration is zero, it is called the equilibrium condition.
∑ F = 0
Where F is the force.
The free body diagram is a diagram of the forces without the details of the bodies, in the attachment we see a free body diagram of each part of the system.
Let's apply the equilibrium condition to each body.
Cat
x-axis
T₂ - T₁ cos θ₁ = 0
T₂ = T₁ cos θ₁
y-axis
T₁ sin θ₁ - \(W_{cat}\) = 0
T₁ sin θ₁ = \(W_[cat}\)
Dog
x-axis
T₃ cos θ₃ - T₂ = 0
T₂ = T₃ cos θ₃
y-axis
T₃ sin θ₃ - \(W_{dog}\)= 0
T₃ sin θ₃ te3 = \(W_{dog}\)
We look for the Tension of cable 2.
T₂ = T₁ cos θ₁
\(W_{cat}\) =T₁ sin θ₁
We solve.
T₂ = \(W_{cat}\) cot θ₁
T₂ = 2.0 9.8 cot 20
T₂ = 53.85 N
We solve the dog equation.
T₂ = T₃ cos θ₃
\(W_{dog}\) = T₃ sin θ₃
We resolve
\(\frac{W_{dog}}{T_2 } = tan \theta_3\)
θ₃ = tan⁻¹ \(\frac{W_{dog}}{T_2}\)
θ₃ = tan⁻¹ ( \(\frac{4.0 \ 9.8 }{53.85}\))
θ₃ = 36º
Now we look for cable 3 tension.
\(W_{dog}\) = T₃ sin θ₃
T₃ = \(\frac{W_{dog}}{sin \theta_3}\)
T₃ = \(\frac{4.0 \ 9.8 }{sin 36}\)
T₃ = 66.7 N
In conclusion using the equilibrium condition we can find the tension in cable 3 is:
T₃ = 66.7 N
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What is sound waves
Sound waves are a type of mechanical wave that propagate through a medium, typically air but also other materials such as water or solids.
Characteristics of sound wavesFrequency: the frequency of a sound wave refers to the number of cycles or vibrations it completes per second and is measured in Hertz (Hz).
Amplitude: the amplitude of a sound wave refers to the maximum displacement or intensity of the wave from its equilibrium position. It represents the loudness or volume of the sound, with larger amplitudes corresponding to louder sounds and smaller amplitudes corresponding to softer sounds.
Wavelength: the wavelength of a sound wave is the distance between two consecutive points in the wave that are in phase, such as from one peak to the next or one trough to the next. It is inversely related to the frequency of the wave.
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The resistivity of a material is 2x10-3Ωm. What is the conductivity\n
Answer:
Conductivity, \(\sigma=500\ (\Omega-m)^{-1}\)
Explanation:
Given that,
The resistivity of a material, \(\rho=2\times 10^{-3}\ \Omega-m\)
We need to find the conductivity of the material.
We know that the reciprocal of resistivity is called conductivity.
\(\sigma=\dfrac{1}{\rho}\\\\\sigma=\dfrac{1}{2\times 10^{-3}}\\\\\sigma=500\ (\Omega-m)^{-1}\)
So, the conductivity of the material is \(500\ (\Omega-m)^{-1}\).
what is kinematics ;-;
explain.
Answer:
the branch of mechanics concerned with the motion of objects without reference to the forces which cause the motion.
Explanation:
EXTREMELY URGENT! DUE IN 15 MINUTES
Answer:
Antibiotics can only kill bacterial infections. they cant treat viruses because it's a viral infection that spreads through the body
They can't be used to treat infections caused by the Corona or any virus because antibiotics only kill bacterial infections. They can not treat Corona or any virus because it's a viral infection that spreads through out the body.
The amplitude of a wave function representing a moving particle can change from positive to negative values in the domain (0, a) over which the wave function is defined. It must therefore pass through zero at some value x0, where 0 < x0 < a. Therefore the probability of the particle being at x0 is zero and the particle can't get from a position x < x0 to a position x > xo.
Required:
Is this reasoning correct?
Answer:
Explanation:
In a standing wave function\(\psi (x,t) = A sin(kx)\) characterized for x between (0.a). on the off chance that the amplitude of the wave interchange from positive to negative at the interval. there probably been a node at \(x_0\), among 0 and a to such an extent that \(0<x_0 <a\). The reasoning is right that the likelihood of discovering the particle at the node \(x_0\) is 0 in light of the fact that by definition, the nodes of the wave are the place where the wave function falls and is equivalent to 0. Since the likelihood of discovering a particle at a position \(x_0\) at time \(t_0\), is provided by \(P=|\psi(x_0,t_0)|^2 dx\), this implies that at the nodes of a standing wave,
\(P = | \psi (x_0,t_0)|^2 \ dx \\ \\ P = |0|^2 dx \\ \\ P = 0\)
So the reasoning that the likelihood of the particle being at \(x_0\) is 0 is right.
However, to examine whether the particle can travel from a position \(x <x_0\) to a position of \(x_0>x\). All together words, can the molecule be found on one or the other side of the node?
The appropriate response is yes.
Recall that in quantum mechanics. wave functions at most present with the likelihood of discovering a particle at a specific time inside a time frame. The wave function doesn't present with an old classical actual trajectory that a particle should follow to go in space: all things being equal, it simply yields chances of whether a particle can be found in a specific spot at a specific time. So the reasoning that a particle can't get from a position \(x <x_0\) to a position of \(x>x_0\), is incorrect.
A thin half ring with a radius of R = 10 cm is uniformly charged with a linear density of = 1 Mikrokulon/m and located in a vacuum. Determine the force F of interaction between the half ring and a point charge q = 20 nC located at the center of curvature. (don't use chatgpt please)
Answer:
Explanation:
F = k * q * lambda * R * π * (1 - √2/2)
Substituting the given values of q, lambda, R, and k, we get:
F = (9 x 10^9 N*m^2/C^2) * (20 x 10^-9 C) * (1 x 10^-6 C/m) * (0.1 m) * π * (1 - √2/2)
F ≈ 8.58 x 10^-4 N
Therefore, the force of interaction between the half ring and the point charge is approximately 8.58 x 10^-4 N.
Light with a wavelength of 5.0 · 10-7 m strikes a surface that requires 2.0 ev to eject an electron. Calculate the energy, in joules, of one incident photon at this frequency. _____ joules 4.0 x 10 -19 4.0 x 10 -49 9.9 x 10 -32 1.1 x 10 -48
Answer:
pretty sure its 6.2 x 10^-13
Explanation:
I looked it up I'm not a bigbrain but want to help
A toy car on a string is pulled across a table horizontally. The string is at an
angle of 30°. Which is the correct free-body diagram for this situation?
EN
w
w
w
w
А
B
с
D
A. A
ОВ. В
ОО Ο Ο
O C. C
D. D
(C)
...........................
Answer:
Hope this helps!
Explanation:
Question 81 point)
Ms. Vetter has not worked out in a long time. She is trying to lift her pet bunny cage off the ground to put into her car for their trip to Bunnyville
to visit some of her pet bunnies ancestors. If Ms. Vetter does not have enough _____ _____ she can use a simple machine to help her lift the cage off the ground and into her car.
A.craft supplies
B.big muscles
C.mechanical force
D.mechanical advantage
Answer:
(C) Mechanical Force
Explanation:
What happens to the domain in this iron nail when the South Pole of a magnet approaches it from the top?
A. All the arrows align to point down
B. All the arrows align to point right
C. All the arrows align to point up
D. All the arrows align to point left
All the arrows align to point down when the South Pole of a magnet approaches it from the top. Therefore, the correct option is option A.
What is magnetic domain?A section of a magnetic substance where the magnetization is uniformly oriented is called a magnetic domain. This indicates that the atoms' individual magnetic moments are lined up with one another and pointing in the same general direction.
The magnetization of such a sample of ferromagnetic spontaneously splits into several tiny areas known as magnetic domains when cooled under a temperature termed the Curie point. All the arrows align to point down when the South Pole of a magnet approaches it from the top
Therefore, the correct option is option A.
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Answer:
All the arrows align to point up. Option C.
Explanation:
Just got it wrong from the other answer and was shown the right answer.
a force acting on a body of mass 24 kg produces an acceleration of 12ms ^-2 . what acceleration will the same force produce in a body of 10 kg
please give answers if they are right and you know how to do it
Answer: a = 28,8
Explanation:
\(F = ma\)
m = 24 , a = 12
\(F=ma\\\\F = 24 x12\\\\F=288\)
Same force :
m = 10
a = ?
F = 288
\(F = ma \\\\288 = 10xa \\\\28,8=a\)
Jane climbs the stairs to the first floor all by herself in a certain time. If the next time she rides the elevator to the first floor then which of the following statements is true?
The work done in both cases are different
the time taken in both cases is the same
the power in both cases is the same.
the work done in both cases is the same.
Answer:
the power in both cases is the same.
Explanation:
hope helps you
thanksss
Part-II Work out Step by step clearly (6%) 5. A 5kg mass starts from rest at xo = -1 and moves under the action of a variable force F(x) = √1-x² to point xf = 1. Calculate the total work done by the force? (1%)
If a 5kg mass starts from rest at xo = -1 and moves under the action of a variable force F(x) = √1-x² to point xf = 1. Then the total work done by the force is equal to π/2 + 1.
To calculate the total work done by the force in this scenario, we can use the formula for work:
Work = ∫F(x) dx
where F(x) is the force as a function of position and dx represents an infinitesimal displacement.
In this case, the force is given by F(x) = √(1 - x²), and we need to find the total work done as the object moves from xo = -1 to xf = 1.
Let's break down the calculation step by step:
Write the integral for work:
Work = ∫F(x) dx
Substitute the given force:
Work = ∫√(1 - x²) dx
Integrate with respect to x:
To integrate the square root of (1 - x²), we use the trigonometric substitution. Let's substitute x = sin(θ) and dx = cos(θ) dθ.
Work = ∫√(1 - sin²(θ)) cos(θ) dθ
Simplify the integrand:
Using the trigonometric identity sin²(θ) + cos²(θ) = 1, we can rewrite the integrand as cos²(θ).
Work = ∫cos²(θ) dθ
Apply the power-reducing formula:
The power-reducing formula states that cos²(θ) = (1 + cos(2θ)) / 2. We can use this formula to simplify the integrand further.
Work = ∫(1 + cos(2θ))/2 dθ
Integrate the terms separately:
Work = (1/2) ∫dθ + (1/2) ∫cos(2θ) dθ
The first integral, ∫dθ, is simply θ, and the second integral, ∫cos(2θ) dθ, can be calculated as sin(2θ)/2.
Work = (1/2) θ + (1/2) (sin(2θ)/2) + C
Evaluate the integral limits:
To find the total work done, we need to evaluate the integral at the upper and lower limits of integration.
At xf = 1, the angle θ is π/2, and at xo = -1, the angle θ is -π/2.
Work = (1/2) (π/2) + (1/2) (sin(2(π/2))/2) - [(1/2) (-π/2) + (1/2) (sin(2(-π/2))/2)]
Simplifying further:
Work = π/4 + (1/2) - (-π/4 + (1/2))
Work = π/4 + 1/2 + π/4 + 1/2
Work = π/2 + 1
Therefore, the total work done by the force is equal to π/2 + 1.
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Two insects are at points 1 and 2. which
of the two insects has the greater kinetic energy of rotation
Atoms do not merely have one layer of electrons. As atoms grow larger, they develop multiple "shells" of electrons, always with an equalnumber of electrons and protons. Many chemical reactions though depend upon the motion of electrons from one atom to another.The graph below shows atomic number (the number of protons and the number of electrons) against ionization energy - the amount ofenergy required to pull an electron off an atom (you can also think of this as the pull between the atom and its outermost electrons). Ateach noble gas (helium, neon, argon, krypton, xenon, radon), a new layer of electrons is added. Use your knowledge of Coulomb's Law toexplain why this trend looks the way it does.
As the ionisation energy is the amount of energy required to remove the outermost electron from an atom.
With the increase in the atomic number, the number of shells are increasing. Due to which the distance between the outer electron and the nucleus is also increasing.
According to the coulomb's law,
\(F=k\frac{q_1q_2}{d^2}\)where F is the force of attraction between the two charges.
In the case of atom,
Let F be the force of attraction between the outer most electron and nucleus.
d is the distance between the nucleus and outermost electron.
As the atomic number increases from helium to radon, the distance between the nucleus and the outermost electron is also increasing.
Thus, the force of attraction between the nucleus and electron decreases.
Hence, the ionisation energy required to remove the outermost electron from helium to radon is decreasing.
A 06-C charge and a .07-C charge are apart at 3 m apart. What force attracts them?
Answer:
the force of attraction between the two charges is 4.2 x 10⁹ N.
Explanation:
Given;
the magnitude of first charge, q₁ = 0.06 C
the magnitude of the second charge, q₂ = 0.07 C
distance between the two charges, r = 3 m
The force of attraction between the two charges is calculated as ;
\(F = \frac{Kq_1q_2}{r^2}\)
where;
k is Coulomb's constant = 9 x 10⁹ Nm²/C²
\(F = \frac{Kq_1q_2}{r^2} \\\\F = \frac{(9\times 10^9)(0.06)(0.07)}{3^2} \\\\F = 4.2 \times 10^{6} \ N\)
Therefore, the force of attraction between the two charges is 4.2 x 10⁹ N.
Which of the following relationships is correct?
2 points
1 N = 1 kg
1 N = 1 kg·m
1 N = 1 kg·m/s
1 N = 1 kg·m/s2
What are the characteristics of a nebulae? (Select all that apply.)
end-stage of a star’s life
contain hydrogen
clouds of gas and dust
location of gas planets
needed to create a star
Answer:
B. contain hydrogen
C. clouds of gas and dust
E. needed to create a star
Explanation:
A star is a giant astronomical or celestial object that is comprised of a luminous sphere of plasma, binded together by its own gravitational force.
Some of the examples of stars are; Vega, Sun (closest to planet Earth), Antares, Betelgeus, Canopus, etc.
Stars are typically made up of two (2) main hot gas, Hydrogen (H) and Helium (He). The chronological order in which the formation of a star occur are;
1. Gravity pulls gas and dust together to form dense cores.
2. A protostar forms as mass increases.
3. Nuclear fusion begins under high pressure.
Scientists have been able to understand and discover that, gravity pulled materials (low-density cloud of interstellar gas and dust known as a nebula) together forming the planetary bodies in our solar system.
A dark nebula can be defined as an interstellar cloud that is so dense as a result of high concentration of gas and dust and as such it obscures the visible wavelengths of light from stars behind it, thus appearing completely opaque (dark patch) in front of a bright emission nebula or in regions having plenty stars.
The characteristics of a nebulae are;
I. It contain hydrogen.
II. Clouds of gas and dust
III. It is needed to create a star.
A motorcycle travels, in one direction only, with an average speed of 916.66 m/min during the first 30 minutes of its travel and 900 m/min during the next 20 minutes.
Calculate (Units must be in units of the international system):
a. The total distance traveled.
b. The average speed.
Explanation:
a. To calculate the total distance traveled, we need to find the distance traveled during the first 30 minutes and the distance traveled during the next 20 minutes, and then add them up.
During the first 30 minutes:
distance = speed × time
distance = 916.66 m/min × 30 min
distance = 27,499.8 meters
During the next 20 minutes:
distance = speed × time
distance = 900 m/min × 20 min
distance = 18,000 meters
Total distance traveled:
distance = 27,499.8 meters + 18,000 meters
distance = 45,499.8 meters
Therefore, the total distance traveled is 45,499.8 meters.
b. To calculate the average speed, we need to divide the total distance traveled by the total time taken.
Total time taken:
time = 30 min + 20 min
time = 50 min
Average speed:
speed = distance ÷ time
speed = 45,499.8 meters ÷ 50 min
speed = 909.996 m/min
Therefore, the average speed is 909.996 m/min.
An AM radio transmitter broadcasts 50.0 kW of power uniformly in all directions. I live 10 km from this station. What is the maximum strength of Electric Field in my house
Answer:
\(E_0=0.173N/C\)
Explanation:
From the question we are told that:
Power \(P=50kw=>50*10^3w\)
Distance \(d=10km=10000m\)
Generally the equation for Intensity is mathematically given by
\(I=\frac{P}{4\pi d^2} w/m^2\)
\(I=\frac{50*10^3}{4 \pi 10000^2} w/m^2\)
\(I=3.98*10^{-5}w/m^2\)
Generally Intensity is also
\(I=\frac{1}{2}cE_0^2e\)
Where
\(e=8.854*10^{-12}Nm^2/c^2\)
Therefore
\(E_0=\sqrt{\frac{2I}{c *e}}\)
\(E_0=\sqrt{\frac{2*3.98*10^{-5}}{3*10^8 *8.854*10^{-12}}}\)
\(E_0=0.173N/C\)
A car of mass 500kg travelling at 60m/s has it speed reduced to 40m/s by a constant breaking force over a distance of 200m. find car initial kinetic energy. the final kinetic energy
Answer:
Ek1 = 900000 [J]
Ek1 = 400000 [J]
Explanation:
In order to solve this problem we must remember that kinetic energy is defined as the product of mass by velocity squared by a medium. Therefore using the following equation we have:
\(E_{k1}=\frac{1}{2}*m*v1^{2}\)
where:
m = mass = 500 [kg]
v1 = 60 [m/s]
So we have:
Ek1 = 0.5*500*(60^2)
Ek1 = 900000 [J]
and:
Ek2 = 0.5*500*(40^2)
Ek2 = 400000 [J]
Question 10 (1 point)
A water wave in a 17 m long pool takes 3 seconds to travel to one end of the pool.
What is the speed of the wave?
Answer:
5.67 m/s
Explanation:
The speed of a wave can be calculated as the distance traveled by the wave divided by the time taken:
Speed = Distance/Time
In this case, the distance traveled by the wave is the length of the pool, which is 17 m. The time taken by the wave to travel this distance is 3 seconds.
So, the speed of the wave can be calculated as:
Speed = 17 m/3 s
Speed = 5.67 m/s
Therefore, the speed of the water wave in the 17 m long pool is 5.67 m/s.
A student drops a rock from rest at a distance h above the ground such that the rock hits the ground at a time t0 . At what distance above the ground should the rock be dropped such that it hits the ground at a time 2t0 after it is released.?
The distance above the ground the rock should be raised in order to hits the ground double of initial time is 4h.
The given parameters;
initial velocity of the rock, u = 0height above the ground, = htime of motion of the rock from the height = t₀The time of motion of the rock from the given height is calculated as;
\(h = ut + \frac{1}{2} gt^2\\\\h = 0 + \frac{1}{2} gt_0^2\\\\h = \frac{1}{2} gt_0^2\\\\t_0^2 = \frac{2h}{g} \\\\t_0 = \sqrt{\frac{2h}{g} }\)
When the time of motion is doubled to 2t₀, the height above the ground should be;
\(2(t_0) = 2(\sqrt{\frac{2h}{g} } )\\\\2(t_0) = \sqrt{\frac{4\times 2h}{g} }\)
Thus, the distance above the ground the rock should be raised in order to hits the ground double of initial time is 4h.
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Compare and contrast, in detail, at least two types of pluralism. Do you think the United States is becoming more pluralistic? Why or why not? How do ethnic enclaves relate to pluralism in the US?
a. There are two main types of pluralism: cultural and political
b. Yes, the United States is becoming more pluralistic
c. Ethnic enclaves can be both a positive and negative aspect of pluralism in the US.
a. Pluralism refers to the coexistence of multiple cultures, religions, and ethnicities within a society. There are two main types of pluralism: cultural and political. Cultural pluralism emphasizes the preservation of distinct cultural traditions, while political pluralism emphasizes the equal representation of different groups within the political system.
Cultural pluralism is often associated with the idea of multiculturalism, which recognizes and celebrates the diversity of different cultures. This type of pluralism acknowledges the importance of cultural differences and encourages individuals to maintain and express their cultural identities. In contrast, political pluralism emphasizes the importance of equal representation of different groups within the political system. This can take the form of proportional representation in government or equal access to political power for different groups.
b. The United States is becoming more pluralistic, as the population becomes more diverse and the importance of multiculturalism and political pluralism is increasingly recognized. The country is home to many different ethnic and cultural groups, and these groups are increasingly visible in politics and society. This is evident in the increasing number of ethnic and cultural enclaves, which are areas where different ethnic groups live in close proximity to one another.
c. Ethnic enclaves can be both a positive and negative aspect of pluralism in the US. On the one hand, they allow individuals to maintain their cultural traditions and create supportive communities. On the other hand, they can also lead to segregation and exclusion, as different groups may be reluctant to interact with one another. In order to promote a positive form of pluralism, it is important to encourage interaction and understanding between different groups, while also respecting and celebrating their distinct cultural identities.
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Find the motor efficiency with 10.0 volts, 0.08 amperes and 05.50 seconds
Answer:
Efficiency is simply output (useful) power divided by input power, with the difference being losses due to imperfections in design and other inevitabilities.
Explanation:
3. A ray of light incident on one face of an equilateral glass prism is refracted in such a way that it emerges from the opposite surface at an angle of 900 to the normal. Calculate the i. angle of incidence. ii. minimum deviation of the ray of light passing through the prism [n_glass=1.52]
Answer:
i) angle of incidence;i = 29.43°
ii) δm = 38.92°
Explanation:
Prism is equilateral so angle of prism (A) = 60°
Refractive index of glass; n_glass = 1.52
A) Let's assume the incident angle = i and Critical angle = θc
We know that, sin θc = 1/n
Thus;
sin θc = 1/n_glass
θc = sin^(-1) (1/n_glass)
θc = sin^(-1) (1/1.52)
θc = 41.14°
Now, the angle of prism will be the sum of external angle that is critical angle and reflected angle.
Thus;
A = r + θc
r = A - θc
So;
r = 60° - 41. 14°
r = 18.86°
From, Snell's law. If we apply it to this question, we will have;
(sin i)/(sin r) = n_glass
Where;
i is angle of incidence and r is angle of reflection.
Let's make i the subject;
i = sin^(-1) (n_glass × sin r)
i = sin^(-1) (1.52 × sin 18.86)
i = sin^(-1) 0.4914
i = 29.43°
B) The formula to calculate minimum deviation would be from;
μ = [sin ((A + δm)/2)]/(sin A/2)
Where;
μ is Refractive index
δm is minimum angle of deviation
A is angle of prism
Now Refractive index is given by a formula; μ = (sin i)/(sin r)
So; μ = (sin 29.43)/(sin 18.86)
μ = 1.52
Thus;
1.52 = [sin ((60 + δm)/2)]/(sin 60/2)
1.52 * sin 30 = sin ((60 + δm)/2)
0.76 = sin ((60 + δm)/2)
sin^(-1) 0.76 = ((60 + δm)/2)
49.46 × 2 = (60 + δm)
98.92 - 60 = δm
δm = 38.92°
can anyone write for me all the equation of linear motion
All the equations of motion are as follows, Displacement (s) equation, Final velocity (v) equation, Average velocity (v_avg) equation, Displacement (s) equation with average velocity, and Displacement (s) equation.
Equations of MotionIn terms of its motion as a function of time, equations of motion define how a physical system behaves. In more detail, the equations of motion define how a physical system behaves as a collection of mathematical functions expressed in terms of dynamic variables.
s = ut + (1/2)at^2v = u + atv_avg = (u + v) / 2s = v_avg * ts = (u + v) / 2 * tv^2 = u^2 + 2asIn conclusion, equations of motion define how a physical system behaves in terms of how its motion changes over time.
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Determine the kinetic energy of the ball immediately after it is hit. (You must provide an answer before moving to the next part.) The kinetic energy of the ball immediately after it is hit is
The question is incomplete. Here is the complete question.
A baseball palyer hits a 5.1 oz baseball with an initial velocity of 140ft/sat an angle of 40° with the horizontal as shown. Determine
a) The kinetic energy of the ball immediately after it is hit
b) The kinetic energy of the ball when it reaches its maximum height
c) The maximum height above the ground reached by the ball.
Answer: a) KE = 131.64 J
b) KE = 0
c) h = 126 ft
Explanation: Kinetic energy is the energy an object posses due to its motion. It can be calculated as \(KE=\frac{1}{2}mv^{2}\)
a) Kinetic energy's unit is Joule. So, we have to transform ounce in kg and ft/s in m/s for the units to correspond:
m = 5.1(0.02835)
m = 0.1445 kg
v = 140 ft = 42.67 m/s
Then, kinetic energy is
\(KE=\frac{1}{2}(0.1445)(42.67)^{2}\)
KE = 131.64 J
Kinetic energy immediately after the ball is hit is 131.64 J.
b) At its maximum height, the ball has its highest potential energy. Because of the law of conservation of energy, when potential energy is maximum, kinetic energy is minimum and vice-versa. So, at the maximum height, kinetic energy is 0.
c) This type of motion is projectile motion. The maximum height on a projectile motion can be determined by
\(v_{y}^{2}=v_{0y}^{2}-2g\Delta y\)
When h is maximum, \(v_{y}=0\)
Velocity of the ball has an angle with the horizontal, so initial velocity at the y-axis is
\(v_{0y}=v_{0}sin(\theta)\)
Substituting and solving
\(v_{y}^{2}=v_{0}^{2}sin^{2}(\theta)-2gh\)
\(0=(42.67)^{2}sin^{2}(40)-2(9.8)h\)
\(19.6h=(42.67)^{2}(0.643)^{2}\)
\(h=\frac{(1820.73)(0.4132)}{19.6}\)
h = 38.4 m
Transforming into ft: h = 126 ft
The maximum height above the ground reached by hte ball is 126 feet.