Q: A projectile is launched at $$v_0 = 50$$\ \mathrm{m/s}$$ at $$\$$theta_0 = 45$$^\circ$$. What is the total time of flight? (g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

$$t = \frac{2 v_0$ \sin \$$theta_0$$}{g} = \frac{2 \times 50 \times \sin 45^\circ}{9.8} \approx 7.2\ \mathrm{s}$$

Question 1

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$\$$theta_0$$ above the horizontal. Which of the following correctly expresses the horizontal and vertical components of the initial velocity?

Accepted Answer

$$v_{0x} = v_0$ \cos \$$theta_0$$, v$$_{0y} = $$v_0$$ \sin \$$theta_0$$

Question 2

A paintball is fired horizontally from a height of $$1.5\ \mathrm{m}$$ with a speed of $$75\ \mathrm{m/s}. $$How long does it take to hit the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$0.553\ \mathrm{s}$$

Question 3

Which equation correctly describes the vertical position $$y of a $$projectile as a function of time $$t$$, initial vertical velocity $$v_{0y}$$, and acceleration due to gravity $$g$$?

Accepted Answer

$$y = v_{0y} t - \frac{1}{2} g t^2$

Question 4

A baseball is hit with an initial speed of $$37\ \mathrm{m/s} at an $$angle of $$53.1^\circ$$ above the horizontal. What is the initial vertical velocity component?

Accepted Answer

$$v_{0y} = 37 \sin 53.1^\circ = 29.6\ \mathrm{m/s}$$

Question 5

In the 'shoot the monkey' demonstration, a hunter aims directly at a monkey hanging from a branch. At the instant the hunter fires, the monkey lets go and falls. If air resistance is negligible, what happens?

Accepted Answer

The projectile will hit the monkey because both fall with the same vertical acceleration.

Question 6

A projectile is launched with an initial velocity $$v_0 at an $$angle $$\$$theta_0$$. What is the time to reach the maximum height?

Accepted Answer

$$t = \frac{v_0$ \sin \$$theta_0$$}{g}$$

Question 7

A projectile is launched from the ground with speed $$v_0 at $$angle $$\$$theta_0$$. What is the formula for its horizontal range (assuming it lands at the same height)?

Accepted Answer

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

Question 8

A ball is thrown horizontally from a $$20\ \mathrm{m}$$ high cliff with a speed of $$10\ \mathrm{m/s}. $$How far from the base of the cliff does the ball land? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\approx 20.2\ \mathrm{m}$$

Question 9

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 10

A projectile is launched with $$v_0 = 20$$\ \mathrm{m/s}$$ at $$\$$theta_0 = 30$$^\circ$$. What is the magnitude of its velocity at the highest point?

Accepted Answer

$$v_0$$ \cos \$$theta_0 = 20$$ \cos 30^\circ = 17.3\ \mathrm{m/s}$$

Question 11

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$\$$theta_0$$. Which equation gives the maximum height reached?

Accepted Answer

$$h = \frac{v_0$^2 \sin^2$ \$$theta_0$$}{2g}$$

Question 12

A projectile is launched at $$v_0 = 50$$\ \mathrm{m/s}$$ at $$\$$theta_0 = 45$$^\circ$$. What is the total time of flight? (g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

Accepted Answer

$$t = \frac{2 v_0$ \sin \$$theta_0$$}{g} = \frac{2 	imes 50 	imes \sin 45^\circ}{9.8} \approx 7.2\ \mathrm{s}$$

Question 13

A projectile is launched horizontally from a height $$h$$ with speed $$v_0. $$Which equation gives the time to hit the ground?

Accepted Answer

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

Question 14

A soccer ball is kicked at $$v_0 = 25$$\ \mathrm{m/s}$$ at $$\$$theta_0 = 40$$^\circ$$. What is the horizontal distance traveled after 2$$\ \mathrm{s}$$? (g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

Accepted Answer

$$x = v_0$ \cos \$$theta_0$$ \cdot t = 25 \cos 40^\circ 	imes 2 \approx 38.3\ \mathrm{m}$$

Question 15

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

Accepted Answer

The horizontal acceleration is zero and the vertical acceleration is $$-g.$$

Question 16

A projectile is launched at $$v_0 = 30$$\ \mathrm{m/s}$$ at $$\$$theta_0 = 60$$^\circ$$. What is the vertical velocity after 2$$\ \mathrm{s}$$? (g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

Accepted Answer

$$v_y = v_0$ \sin \$$theta_0$$ - g t = 30 \sin 60^\circ - 9.8 	imes 2 \approx 25.98 - 19.6 = 6.38\ \mathrm{m/s}$$

Question 17

A projectile is launched from the ground with $$v_0 = 15$$\ \mathrm{m/s}$$ at $$\$$theta_0 = 90$$^\circ$$. What is the horizontal range?

Accepted Answer

$$0\ \mathrm{m}$$

Projectile Motion: Motion in a Plane

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