Q: A ball is launched horizontally from a 2-meter-tall table with a speed of 3.0 m/s. How long does it take for the ball to hit the ground? Use $$g = 9.8\ \mathrm{m/s^2$}.$$

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 2}{9.8}} \approx 0.64\ \mathrm{s}$$

Q: A projectile is launched at $$20\ \mathrm{m/s} at an $$angle of $$53^\circ$$ above the horizontal and returns to the ground. What is the total time of flight? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \frac{2v_0\sin\theta}{g} = \frac{2 \times 20 \times \sin(53^\circ)}{9.8} \approx 3.3\ \mathrm{s}$$

Q: A water spout shoots water straight downwards. The magnitude of the water's velocity when it hits the ground is $$14\ \mathrm{m/s}. $$How high is the spout from the ground? (Assume $$v_0 = 0$, g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

$$h = \frac{v^2$}{2g} = \frac{14^2$}{2 \times 9.8} \approx 10\ \mathrm{m}$$

Q: A football is kicked at $$20\ \mathrm{m/s} at an $$angle of $$53^\circ$$ above the horizontal. What is the vertical component of the football's velocity when it returns to the ground?

$$v_{y,final} = -v_{y,initial} = -v_0$\sin\theta = -20\sin(53^\circ) \approx -16\ \mathrm{m/s}$$

Q: A projectile is launched upwards at $$30\ \mathrm{m/s}$$ from ground level at an angle $$65^\circ$$ above the horizontal. What is the maximum horizontal distance it can travel before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$R = \frac{v_0$^2 \sin(2\theta)}{g} = \frac{30^2$ \sin(130^\circ)}{9.8} \approx 84.4\ \mathrm{m}$$

Question 1

A ball is launched horizontally from a 2-meter-tall table with a speed of 3.0 m/s. How long does it take for the ball to hit the ground? Use $$g = 9.8\ \mathrm{m/s^2$}.$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 2}{9.8}} \approx 0.64\ \mathrm{s}$$

Question 2

Which of the following best describes the acceleration of a projectile in 2D motion after launch (neglecting air resistance)?

Accepted Answer

It is always directed downward with magnitude $$g$$

Question 3

A rock is thrown downward from a building at $$5\ \mathrm{m/s} at an $$angle of $$37^\circ$$ below the horizontal. If it lands $$10\ \mathrm{m}$$ from the base of the building, what is the height of the building? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{1}{2}gt^2$ + v$$_{y0}$$t$$,\ where\ v_{y0} = 5\sin(37^\circ)$$,\ solve for t$ using x$$ = $$v_{x0}t$ and v$$_{x0} = 5\cos(37^\circ)$$,\ final answer: h$$ \approx 10.6\ \mathrm{m}$

Question 4

A projectile is launched at $$20\ \mathrm{m/s} at an $$angle of $$53^\circ$$ above the horizontal and returns to the ground. What is the total time of flight? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \frac{2v_0\sin	heta}{g} = \frac{2 	imes 20 	imes \sin(53^\circ)}{9.8} \approx 3.3\ \mathrm{s}$$

Question 5

A cannonball is fired horizontally from a cliff $$100\ \mathrm{m}$$ above the ground with a speed of $$20\ \mathrm{m/s}. $$What horizontal distance does the cannonball travel before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

Question 6

A water spout shoots water straight downwards. The magnitude of the water's velocity when it hits the ground is $$14\ \mathrm{m/s}. $$How high is the spout from the ground? (Assume $$v_0 = 0$, g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{14^2$}{2 	imes 9.8} \approx 10\ \mathrm{m}$$

Question 7

A football is kicked at $$20\ \mathrm{m/s} at an $$angle of $$53^\circ$$ above the horizontal. What is the vertical component of the football's velocity when it returns to the ground?

Accepted Answer

$$v_{y,final} = -v_{y,initial} = -v_0$\sin	heta = -20\sin(53^\circ) \approx -16\ \mathrm{m/s}$$

Question 8

A car carrying a vertical missile launcher moves horizontally at $$60\ \mathrm{m/s} to $$the right. The missile launches vertically upward at $$80\ \mathrm{m/s}. $$What is the magnitude of the velocity of the missile just after launch?

Accepted Answer

$$v_{missile} = \sqrt{v_{x}^2 + v_{y}^2} = \sqrt{60^2$ + 80^2$} = 100\ \mathrm{m/s}$$

Question 9

A ball is thrown over a net that is $$1.6\ \mathrm{m}$$ away and $$0.90\ \mathrm{m}$$ above the floor. What initial speed does the ball need to just clear the net if thrown horizontally?

Accepted Answer

Question 10

A projectile is launched upwards at $$30\ \mathrm{m/s}$$ from ground level at an angle $$65^\circ$$ above the horizontal. What is the maximum horizontal distance it can travel before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$R = \frac{v_0$^2 \sin(2	heta)}{g} = \frac{30^2$ \sin(130^\circ)}{9.8} \approx 84.4\ \mathrm{m}$$

Question 11

A ball is dropped from rest and lands on a car that accelerates uniformly forwards from rest. If the ball lands on the car after $$2\ \mathrm{s}$$ and the car travels $$8\ \mathrm{m} in $$that time, what was the acceleration of the car?

Accepted Answer

$$x = \frac{1}{2}at^2$ \Rightarrow a = \frac{2x}{t^2$} = \frac{2 	imes 8}{2^2$} = 4\ \mathrm{m/s^2$}$$

Question 12

A projectile is launched from a moving vehicle. If the vehicle moves at $$v_{veh}$$ and the projectile is launched at $$v_{proj}$$ relative to the vehicle, what is the total velocity of the projectile relative to the ground?

Accepted Answer

$$v_{total} = v_{veh} + v_{proj} ($$vector sum)

Question 13

Which equation would you use to find the time it takes for a projectile to reach its maximum height when launched upwards at $$v_0$$ and angle $$	heta$$?

Accepted Answer

$$v_{y} = v_{y0} - gt$$,\ set $$v_{y} = 0 at $$max height,\ so $$t = \frac{v_{y0}}{g} = \frac{v_0$ \sin	heta}{g}$$

Question 14

A projectile is launched at $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the formula for its maximum height?

Accepted Answer

$$h_{max} = \frac{v_0$^2 \sin^2$	heta}{2g}$$

Question 15

A ball is launched horizontally from a cliff and lands $$24.5\ \mathrm{m}$$ from the base. If the initial speed is $$5\ \mathrm{m/s}$$, how tall is the cliff? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

Question 16

A projectile is launched from the ground and lands $$32\ \mathrm{m}$$ away after $$8\ \mathrm{s}. $$What is the magnitude of the gravitational acceleration on this planet?

Accepted Answer

$$g = \frac{2v_{y0}}{t}$$,\ but since $$x = v$$_{x0}$$t$$,\ $$v_{x0} = \frac{32}{8} = 4\ \mathrm{m/s}$$,\ use $$y = v$$_{y0}$$t - \frac{1}{2}gt^2$ = 0$$,\ so $$g = \frac{2v_{y0}t}{t^2$}$$,\ but $$v_{y0} = 0$$,\ so $$g = 0.3\ \mathrm{m/s^2$}$$

Question 17

Which of the following is true for the horizontal and vertical components of projectile motion (neglecting air resistance)?

Accepted Answer

Horizontal acceleration is zero; vertical acceleration is $$-g$$

Question 18

A projectile is launched upwards and returns to the same height from which it was launched. What is true about its trajectory?

Accepted Answer

The trajectory is symmetrical; time up equals time down

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