Q: Which equation correctly gives the range $R$ of a projectile launched at speed $v_0$ and angle $\theta$ (assuming symmetric trajectory and no air resistance)?

$R = \dfrac{v_0^2 \sin2\theta}{g}$

Q: A ball is thrown with initial velocity $v_0$ at angle $\theta$. Which pair of angles will result in the same range, assuming symmetric trajectory and no air resistance?

$\theta$ and $90^\circ - \theta$

Question 1

A soccer ball is kicked from ground level with an initial velocity of $v_0 = 20\ \mathrm{m/s}$ at an angle of $30^\circ$ above the horizontal. Neglecting air resistance, what is the maximum height reached by the ball?

Accepted Answer

$h_{max} = \dfrac{(20\sin30^\circ)^2}{2g}$

Question 2

Which of the following statements about average velocity in two-dimensional motion is correct?

Accepted Answer

Average velocity is independent of the path taken and depends only on displacement.

Question 3

A particle moves in a circle of radius $r$ at constant speed $v$. What is the magnitude of its centripetal acceleration?

Accepted Answer

$a_c = \dfrac{v^2}{r}$

Question 4

A projectile is launched at an angle $	heta$ with initial speed $v_0$. For which angle is the range maximized, assuming symmetric trajectory and no air resistance?

Accepted Answer

$	heta = 45^\circ$

Question 5

A car moves east at $20\ \mathrm{m/s}$ on a moving walkway that travels east at $5\ \mathrm{m/s}$. What is the car's velocity relative to a stationary observer?

Accepted Answer

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

Question 6

Which of the following correctly expresses the position vector $\vec{r}$ of a particle moving in the $xy$-plane under constant acceleration?

Accepted Answer

$\vec{r} = \vec{r}_0 + \vec{v}_0 t + \dfrac{1}{2}\vec{a}t^2$

Question 7

A ball is thrown horizontally from a cliff with speed $v_0$. Which statement about its motion is correct (neglecting air resistance)?

Accepted Answer

The horizontal velocity remains constant while the vertical velocity increases linearly with time.

Question 8

A cyclist moves north at $10\ \mathrm{m/s}$ while a wind blows east at $5\ \mathrm{m/s}$. What is the magnitude of the cyclist's velocity relative to the ground?

Accepted Answer

$\sqrt{10^2 + 5^2} = 11.18\ \mathrm{m/s}$

Question 9

Which of the following is true about the acceleration of a projectile at the highest point of its trajectory (neglecting air resistance)?

Accepted Answer

The acceleration is directed downward and equals $g$.

Question 10

A train moves at $30\ \mathrm{m/s}$ east. A passenger walks at $2\ \mathrm{m/s}$ west inside the train. What is the passenger's velocity relative to the ground?

Accepted Answer

$28\ \mathrm{m/s}$\ east

Question 11

Which equation correctly gives the range $R$ of a projectile launched at speed $v_0$ and angle $	heta$ (assuming symmetric trajectory and no air resistance)?

Accepted Answer

$R = \dfrac{v_0^2 \sin2	heta}{g}$

Question 12

In uniform circular motion, what is the direction of the centripetal acceleration vector?

Accepted Answer

Toward the center of the circle

Question 13

A stone is thrown at $v_0 = 15\ \mathrm{m/s}$ at $60^\circ$ above the horizontal. What is the initial vertical component of velocity?

Accepted Answer

$v_{0y} = 15\sin60^\circ$

Question 14

Which of the following best describes the instantaneous velocity vector at any point along a curved path?

Accepted Answer

It is tangent to the path at that point and in the direction of motion.

Question 15

A ball is thrown with initial velocity $v_0$ at angle $	heta$. Which pair of angles will result in the same range, assuming symmetric trajectory and no air resistance?

Accepted Answer

$	heta$ and $90^\circ - 	heta$

Question 16

Which of the following is a correct statement about the independence of motion in two dimensions?

Accepted Answer

Motion in the $x$ and $y$ directions can be analyzed independently.

Question 17

A runner moves at $6\ \mathrm{m/s}$ north on a moving walkway going $2\ \mathrm{m/s}$ south. What is the runner's velocity relative to the ground?

Accepted Answer

$4\ \mathrm{m/s}$\ north

Question 18

Which of the following is the correct expression for instantaneous acceleration?

Accepted Answer

$a = \dfrac{dv}{dt}$

Question 19

A car travels in a circle of radius $10\ \mathrm{m}$ at a speed of $5\ \mathrm{m/s}$. What is the period $T$ of one revolution?

Accepted Answer

$T = \dfrac{2\pi 	imes 10}{5}$

(CH3) Kinematics in Two Dimensions: Position, Velocity, and Acceleration

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