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

$R = \frac{v_0^2 \sin(2\theta)}{g}$

Q: A football is kicked at $v_0 = 20$ m/s at $45^\circ$ above the horizontal. What is the maximum height reached by the ball?

$h = \frac{v_0^2 \sin^2(\theta)}{2g}$

Q: A ball is thrown with velocity $v_0$ at angle $\theta$. What is the time of flight until it returns to the same vertical level?

$T = \frac{2 v_0 \sin \theta}{g}$

Q: A projectile is launched at $v_0$ and $\theta$. What is the formula for its velocity vector at time $t$?

$\vec{v}(t) = v_0 \cos \theta \hat{i} + (v_0 \sin \theta - g t) \hat{j}$

Question 1

A soccer ball is kicked from the ground with an initial velocity of $v_0$ at an angle $	heta$ above the horizontal. Neglecting air resistance, which of the following correctly describes the acceleration of the ball during its flight?

Accepted Answer

The acceleration is $a_x = 0$ and $a_y = -g$ at all times.

Question 2

Given a position vector $\vec{r} = x \hat{i} + y \hat{j}$, what is the magnitude of $\vec{r}$?

Accepted Answer

$|\vec{r}| = \sqrt{x^2 + y^2}$

Question 3

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

Accepted Answer

$R = \frac{v_0^2 \sin(2	heta)}{g}$

Question 4

Which statement best describes the instantaneous velocity vector of a particle moving along a curved path in the $xy$-plane?

Accepted Answer

It is always tangent to the path at the particle's position.

Question 5

A projectile is launched with initial velocity components $v_{0x}$ and $v_{0y}$. What is the velocity in the $y$-direction at time $t$?

Accepted Answer

$v_y(t) = v_{0y} - gt$

Question 6

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

Accepted Answer

$5.0$ m/s

Question 7

Which of the following is true about the acceleration vector for a particle moving in a plane?

Accepted Answer

It can change due to a change in magnitude and/or direction of velocity.

Question 8

A projectile is fired horizontally from a cliff with speed $v_0$. What is its vertical displacement after time $t$?

Accepted Answer

$y = \frac{1}{2} g t^2$

Question 9

If a vector $\vec{A}$ has components $A_x = 3$ and $A_y = 4$, what is the angle $	heta$ it makes with the $x$-axis?

Accepted Answer

$	heta = \arctan(4/3)$

Question 10

A paintball is fired at $v_0 = 50$ m/s at an angle $	heta = 30^\circ$ above the horizontal. What is the initial vertical component of velocity?

Accepted Answer

$v_{0y} = v_0 \sin(30^\circ)$

Question 11

A football is kicked at $v_0 = 20$ m/s at $45^\circ$ above the horizontal. What is the maximum height reached by the ball?

Accepted Answer

$h = \frac{v_0^2 \sin^2(	heta)}{2g}$

Question 12

Which of the following best describes the method for subtracting two vectors $\vec{A}$ and $\vec{B}$?

Accepted Answer

Add $\vec{A}$ and the negative of $\vec{B}$.

Question 13

A runner moves with velocity $\vec{v}_1$ relative to the ground, while the ground moves with velocity $\vec{v}_2$ relative to a train. What is the runner's velocity relative to the train?

Accepted Answer

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

Question 14

A projectile is launched at $v_0$ and $	heta$. At what point in its trajectory is its speed minimum?

Accepted Answer

At the highest point of the trajectory.

Question 15

Which equation gives the position in the $x$-direction for a projectile launched with initial velocity $v_{0x}$?

Accepted Answer

$x(t) = x_0 + v_{0x} t$

Question 16

A ball is thrown with velocity $v_0$ at angle $	heta$. What is the time of flight until it returns to the same vertical level?

Accepted Answer

$T = \frac{2 v_0 \sin 	heta}{g}$

Question 17

A projectile is launched at $v_0$ and $	heta$. What is the formula for its velocity vector at time $t$?

Accepted Answer

$\vec{v}(t) = v_0 \cos 	heta \hat{i} + (v_0 \sin 	heta - g t) \hat{j}$

Question 18

A ball is thrown horizontally from a height $h$ with speed $v_0$. How long does it take to hit the ground?

Accepted Answer

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

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

Study Guide - Practice Questions

Study Guide - Flashcards