Q: For a projectile launched at an angle $\theta_0$ with initial speed $v_0$, what is the formula for the range $R$ (horizontal distance traveled) on level ground?

$R = \dfrac{v_0^2 \sin 2\theta_0}{g}$

Question 1

A ball is thrown horizontally from the top of a 45.0 m tall building and lands 24.0 m from the base. What was the ball’s initial speed?

Accepted Answer

$7.92\ \mathrm{m/s}$

Question 2

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

Accepted Answer

A parabola

Question 3

A tiger leaps horizontally from a 6.5 m high rock with a speed of $3.5\ \mathrm{m/s}$. How far from the base of the rock will she land? (Use $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$4.0\ \mathrm{m}$

Question 4

A football is kicked at ground level with a speed of $18.0\ \mathrm{m/s}$ at an angle of $35.0^\circ$ to the horizontal. How long is the ball in the air before it lands? (Use $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$2.10\ \mathrm{s}$

Question 5

For a projectile launched at an angle $	heta_0$ with initial speed $v_0$, what is the formula for the range $R$ (horizontal distance traveled) on level ground?

Accepted Answer

$R = \dfrac{v_0^2 \sin 2	heta_0}{g}$

Question 6

A pilot flying horizontally at $180\ \mathrm{km/h}$ wants to drop supplies to victims on the ground $160\ \mathrm{m}$ below. How many seconds before the plane is directly overhead should the supplies be released? (Use $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$2.86\ \mathrm{s}$

Question 7

Which of the following statements about projectile motion is correct?

Accepted Answer

The vertical acceleration is constant and equal to $g$.

Question 8

An athlete executes a long jump at a $28.0^\circ$ angle and travels $7.80\ \mathrm{m}$. What was the takeoff speed? (Use $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$8.60\ \mathrm{m/s}$

Question 9

If the takeoff speed in the previous long jump problem is increased by $5.0\%$, how much longer would the jump be?

Accepted Answer

$8.97\ \mathrm{m}$

Question 10

A ball is thrown horizontally from a cliff and lands a certain distance away. If the height of the cliff is doubled, what happens to the horizontal distance (range), assuming the initial speed is unchanged?

Accepted Answer

It increases by a factor of $\sqrt{2}$.

Question 11

Which kinematic equation correctly describes the vertical position $y$ of a projectile as a function of time $t$ (assuming upward is positive and $y_0$ is the initial height)?

Accepted Answer

$y = y_0 + v_{y0} t - \dfrac{1}{2} g t^2$

Question 12

A projectile is launched at an angle $	heta_0$ with initial speed $v_0$. What is the vertical component of its initial velocity?

Accepted Answer

$v_0 \sin 	heta_0$

Question 13

A projectile is launched at $20.0\ \mathrm{m/s}$ at an angle of $45.0^\circ$ above the horizontal. What is the maximum height it reaches? (Use $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$10.2\ \mathrm{m}$

Question 14

Which of the following is true about the velocity of a projectile at the highest point of its trajectory?

Accepted Answer

The vertical component of velocity is zero.

Question 15

A ball is thrown horizontally from a building. Which of the following best describes its acceleration during flight (neglecting air resistance)?

Accepted Answer

Constant and downward, equal to $g$

Question 16

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

Accepted Answer

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

Question 17

A projectile is launched at $v_0$ and angle $	heta_0$. Which of the following would increase the range of the projectile, assuming all other factors remain constant?

Accepted Answer

Increasing the launch angle from $30^\circ$ to $45^\circ$

Question 18

A ball is thrown horizontally from a building and lands 30 m from the base. If the initial speed is doubled, how far from the base will it land (assuming the same height)?

Accepted Answer

60 m

Projectile Motion: Concepts and Problem Solving (Giancoli Physics, Chapter 3)

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