Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the formula for its initial velocity components?

$$v_{x,0} = v_0$ \cos\theta$$, $$v_{y,0} = v_0$ \sin\theta$$

Question 1

A train is moving east at $$30\ \mathrm{m/s}$$, and a passenger walks west inside the train at $$5\ \mathrm{m/s}$$ relative to the train. What is the passenger's velocity relative to an observer standing on the ground?

Accepted Answer

$$25\ \mathrm{m/s}$$\ east

Question 2

Which equation correctly expresses the Galilean transformation of velocity between two frames moving at constant velocity relative to each other?

Accepted Answer

$$\vec{v} = \vec{w} + \vec{v}_F$$

Question 3

A ball is launched vertically upward from a cart moving horizontally at $$v_{\mathrm{cart}}. $$Where will the ball land relative to the cart (ignoring air resistance)?

Accepted Answer

Right into the cart

Question 4

A drone flying horizontally at $$15\ \mathrm{m/s}$$ drops a package from an altitude of $$40\ \mathrm{m}. $$What is the horizontal distance the package travels before hitting the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ and neglect air resistance.)

Accepted Answer

$$43\ \mathrm{m}$$

Question 5

Which of the following statements about Galilean transformations is TRUE?

Accepted Answer

They are only valid for frames moving at constant velocity relative to each other.

Question 6

A ball is thrown upward from a cart moving at $$v_{\mathrm{cart}}$$ horizontally. What are the $$x$$ and $$y$$ components of the initial velocity of the ball as seen from the ground?

Accepted Answer

$$v_{x,0} = v_{\mathrm{cart}},\ v_{y,0} = v_{\mathrm{up}}$$

Question 7

A projectile is launched horizontally from a cliff of height $$h$$ with initial speed $$v_0. $$What is the time it takes to hit the ground?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 8

A person on a moving walkway walks forward at $$2\ \mathrm{m/s}$$ relative to the walkway, which itself moves at $$3\ \mathrm{m/s}$$ relative to the ground. What is the person's velocity relative to the ground?

Accepted Answer

$$5\ \mathrm{m/s}$$

Question 9

Which of the following best describes projectile motion under the influence of gravity (neglecting air resistance)?

Accepted Answer

It is two-dimensional motion with constant acceleration downward.

Question 10

A ball is thrown horizontally from a moving cart at $$v_{\mathrm{cart}} to $$the right. If the ball is thrown with speed $$v_{\mathrm{throw}} to $$the left (relative to the cart), what is its velocity relative to the ground?

Accepted Answer

$$v_{\mathrm{cart}} - v_{\mathrm{throw}}$$

Question 11

A food package is dropped from a plane flying horizontally at $$v_0$$ and altitude $$h. $$What is the $$x$$ component of the initial velocity of the package?

Accepted Answer

$$v_{x,0} = v_0$

Question 12

Which of the following is a key assumption for using Galilean transformations in kinematics?

Accepted Answer

Relative motion is at constant velocity.

Question 13

A ball is thrown upward from a cart moving at $$10\ \mathrm{m/s} to $$the right. If the ball is in the air for $$2\ \mathrm{s}$$, how far does the cart move during this time?

Accepted Answer

$$20\ \mathrm{m}$$

Question 14

If a ball is thrown upward from a moving cart, which of the following best explains why it lands back in the cart?

Accepted Answer

The ball retains the horizontal velocity of the cart throughout its flight.

Question 15

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the formula for its initial velocity components?

Accepted Answer

$$v_{x,0} = v_0$ \cos	heta$$, $$v_{y,0} = v_0$ \sin	heta$$

Question 16

Which of the following is NOT a consequence of using an accelerating frame of reference in kinematics?

Accepted Answer

Projectile motion equations remain unchanged.

Question 17

A ball is thrown horizontally from a height $$h$$ with speed $$v_0. $$What is the equation for its horizontal displacement when it hits the ground?

Accepted Answer

$$x = v_0$ \sqrt{\dfrac{2h}{g}}$$

Question 18

Which of the following best describes the acceleration of a projectile in the horizontal direction (neglecting air resistance)?

Accepted Answer

$$a_x = 0$$

Kinematics in Multiple Dimensions and Relative Velocity: Study Notes

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