Q: A projectile is launched with an initial speed $v_0$ at an angle $\theta$ above the horizontal. What is the formula for the range $R$ of the projectile (neglecting air resistance)?

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

Question 1

A soccer ball is kicked from the ground with an initial velocity of $20\ \mathrm{m/s}$ at an angle of $30^\circ$ above the horizontal. Neglecting air resistance, what is the maximum height reached by the ball? (Use $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$5.1\ \mathrm{m}$

Question 2

Which of the following statements about projectile motion is correct?

Accepted Answer

The horizontal and vertical motions are independent except for sharing the same time of flight.

Question 3

A ball is thrown horizontally from a $45\ \mathrm{m}$ high cliff with a speed of $10\ \mathrm{m/s}$. How far from the base of the cliff does the ball land? (Neglect air resistance, $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$30.3\ \mathrm{m}$

Question 4

Given a velocity vector $\vec{v}$ with components $v_x = 6\ \mathrm{m/s}$ and $v_y = 8\ \mathrm{m/s}$, what is the magnitude of $\vec{v}$?

Accepted Answer

$10\ \mathrm{m/s}$

Question 5

A model car moves from point $P_1$ at $(2.0\ \mathrm{s},\ 4.0\ \mathrm{m},\ 2.0\ \mathrm{m})$ to point $P_2$ at $(2.5\ \mathrm{s},\ 7.0\ \mathrm{m},\ 6.0\ \mathrm{m})$. What is the $y$-component of the average velocity?

Accepted Answer

$8.0\ \mathrm{m/s}$

Question 6

Which of the following best describes the instantaneous velocity vector of a particle moving along a curved path?

Accepted Answer

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

Question 7

A projectile is launched with an initial speed $v_0$ at an angle $	heta$ above the horizontal. What is the formula for the range $R$ of the projectile (neglecting air resistance)?

Accepted Answer

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

Question 8

A baseball is hit at ground level with a speed of $40\ \mathrm{m/s}$ at an angle of $45^\circ$. What is the total time the ball spends in the air? (Use $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$5.8\ \mathrm{s}$

Question 9

Which of the following is true about the acceleration of a projectile in flight (neglecting air resistance)?

Accepted Answer

The acceleration is constant and directed downward.

Question 10

A boat moves east at $5\ \mathrm{m/s}$ relative to the water, while the river flows north at $3\ \mathrm{m/s}$. What is the boat's speed relative to an observer on the shore?

Accepted Answer

$5.8\ \mathrm{m/s}$

Question 11

A projectile is launched from the ground with an initial velocity of $v_0$ at an angle $	heta$ above the horizontal. What is the initial vertical component of velocity?

Accepted Answer

$v_0 \sin 	heta$

Question 12

A football is kicked at $25\ \mathrm{m/s}$ at an angle of $37^\circ$ above the horizontal. What is the horizontal component of its initial velocity?

Accepted Answer

$20\ \mathrm{m/s}$

Question 13

Which of the following best describes the process of vector addition using the head-to-tail method?

Accepted Answer

Place the tail of the second vector at the head of the first; the resultant is from the tail of the first to the head of the second.

Question 14

A projectile is launched at $v_0$ and angle $	heta$. At the peak of its trajectory, which statement is true?

Accepted Answer

The vertical component of velocity is zero.

Question 15

A car travels $100\ \mathrm{m}$ east, then $100\ \mathrm{m}$ north. What is the magnitude of its displacement from the starting point?

Accepted Answer

$141\ \mathrm{m}$

Question 16

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

Accepted Answer

$126.9^\circ$

Question 17

Which of the following is a correct statement about average acceleration in two dimensions?

Accepted Answer

Average acceleration is the change in velocity vector divided by the time interval.

Question 18

A projectile is fired at $60^\circ$ above the horizontal with a speed of $50\ \mathrm{m/s}$. What is the time to reach the maximum height? ($g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$4.4\ \mathrm{s}$

Question 19

A rescue plane flying horizontally at $60\ \mathrm{m/s}$ drops a package from a height of $180\ \mathrm{m}$. Where does the package land relative to the point directly below where it was released? ($g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$360\ \mathrm{m}$

Motion in a Plane: Position, Velocity, and Acceleration in Two Dimensions

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