Q: A soccer ball is kicked from the ground with an initial velocity of $$v_0 at an $$angle $$\theta$$ above the horizontal. Which of the following correctly expresses the initial velocity components in the $$x$$ and $$y$$ directions?

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

Q: A baseball is hit with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the formula for the range $$R of $$the projectile (assuming it lands at the same height it was launched)?

$$R = \dfrac{v_0$^2 \sin 2\theta}{g}$$

Q: Which of the following is true about the average acceleration vector in two-dimensional motion?

It is defined as $$\vec{a}_{\text{av}} = \dfrac{\Delta \vec{v}}{\Delta t}.$$

Q: Which of the following is the correct formula for the instantaneous acceleration vector?

$$\vec{a} = \lim_{\Delta t \to 0} \dfrac{\Delta \vec{v}}{\Delta t}$$

Q: A ball is thrown with velocity $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the formula for its vertical position $$y(t) at $$time $$t$$?

$$y(t) = y_0$ + v_0$ \sin \theta \cdot t - \dfrac{1}{2}gt^2$

Question 1

A soccer ball is kicked from the ground with an initial velocity of $$v_0 at an $$angle $$	heta$$ above the horizontal. Which of the following correctly expresses the initial velocity components in the $$x$$ and $$y$$ directions?

Accepted Answer

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

Question 2

A projectile is launched horizontally from a cliff of height $$h$$ with initial speed $$v_0. $$Neglecting air resistance, what is the time $$t it $$takes to hit the ground?

Accepted Answer

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

Question 3

Which statement about the instantaneous velocity vector of a particle moving in a plane is correct?

Accepted Answer

It is always tangent to the path.

Question 4

A baseball is hit with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the formula for the range $$R of $$the projectile (assuming it lands at the same height it was launched)?

Accepted Answer

$$R = \dfrac{v_0$^2 \sin 2	heta}{g}$$

Question 5

A model car moves from point $$P_1 at$$ $$(4.0\,	ext{m}, 2.0\,	ext{m}) to $$point $$P_2 at$$ $$(7.0\,	ext{m}, 6.0\,	ext{m}) in$$ $$0.5\,	ext{s}. $$What is the magnitude of its average velocity?

Accepted Answer

$$5.0\,	ext{m/s}$$

Question 6

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

Accepted Answer

It is $$-g in $$the $$y$$ direction and zero in the $$x$$ direction.

Question 7

A ball is thrown with velocity $$v_0 at an $$angle $$	heta$$ above the horizontal. At the highest point of its trajectory, what is the vertical component of its velocity?

Accepted Answer

$$0$$

Question 8

If a vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4$$, what is its magnitude?

Accepted Answer

$$5$$

Question 9

A paintball is fired horizontally from a height of $$1.5\,	ext{m}$$ with a speed of $$20\,	ext{m/s}. $$How far from the base of the wall will it land?

Accepted Answer

$$7.8\,	ext{m}$$

Question 10

Which of the following is true about the average acceleration vector in two-dimensional motion?

Accepted Answer

It is defined as $$\vec{a}_{	ext{av}} = \dfrac{\Delta \vec{v}}{\Delta t}.$$

Question 11

A runner moves with velocity $$\vec{v}_1$$ relative to the ground. If the ground itself moves with velocity $$\vec{v}_2$$ relative to a stationary observer, what is the runner's velocity relative to the observer?

Accepted Answer

$$\vec{v}_1 + \vec{v}_2$$

Question 12

A projectile is launched at $$30^\circ$$ above the horizontal with a speed of $$50\,	ext{m/s}. $$What is the maximum height reached by the projectile?

Accepted Answer

$$31.9\,	ext{m}$$

Question 13

Which of the following is the correct formula for the instantaneous acceleration vector?

Accepted Answer

$$\vec{a} = \lim_{\Delta t 	o 0} \dfrac{\Delta \vec{v}}{\Delta t}$$

Question 14

A football is kicked at an angle of $$45^\circ$$ with an initial speed of $$20\,	ext{m/s}. $$What is the time of flight before it lands at the same height?

Accepted Answer

$$2.88\,	ext{s}$$

Question 15

Which of the following statements about projectile motion is correct?

Accepted Answer

The horizontal and vertical motions are independent except for time.

Question 16

A vector $$\vec{A} is $$subtracted from vector $$\vec{B} by $$adding the opposite of $$\vec{A}. $$Which of the following represents $$\vec{B} - \vec{A}$$?

Accepted Answer

$$\vec{B} + (-\vec{A})$$

Question 17

A baseball is hit horizontally from a height of $$1.0\,	ext{m}$$ and lands $$20.0\,	ext{m}$$ away. What was its initial speed?

Accepted Answer

$$14.2\,	ext{m/s}$$

Question 18

If a projectile is launched at an angle $$	heta$$ and lands at the same height, at what angle is the range maximized?

Accepted Answer

$$45^\circ$$

Question 19

A ball is thrown with velocity $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the formula for its vertical position $$y(t) at $$time $$t$$?

Accepted Answer

$$y(t) = y_0$ + v_0$ \sin 	heta \cdot t - \dfrac{1}{2}gt^2$

Motion in a Plane – Study Notes (College Physics, Chapter 3)

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