Q: A tennis player standing 12.6 m from the net hits the ball at $$3.00^\\circ$$ above the horizontal. To just clear the net, the ball must rise at least 0.350 m. If the ball just clears the net at the apex of its trajectory, what is the minimum initial speed the player must give the ball? (Assume $$g = 9.8 \\ \mathrm{m/s^2$}.)$$

$$v_0 = 22.0$$ \\ \mathrm{m/s}$$

Q: An astronaut on a strange planet finds that she can jump a maximum horizontal distance of $$15.0 \\ \mathrm{m} if $$her initial speed is $$3.00 \\ \mathrm{m/s}. $$What is the free-fall acceleration on this planet?

$$g = 0.60 \\ \mathrm{m/s^2$}$$

Q: A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. Which of the following expressions gives the maximum height $$H$$ reached by the projectile?

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

Q: If a projectile is launched at an angle $$\theta$$ and lands at the same height from which it was launched, which of the following gives the total time of flight $$T$$?

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

Q: A projectile is launched at $$60.0^\\circ$$ with an initial speed of $$50.0 \\ \mathrm{m/s}. $$What is the vertical component of its initial velocity?

$$v_{0y} = 43.3 \\ \mathrm{m/s}$$

Q: A projectile is launched from a height $$h$$ above the ground with initial speed $$v_0 at an $$angle $$\theta. $$Which equation gives the total time of flight?

$$t = \dfrac{v_0$ \sin \theta}{g} + \sqrt{\left(\dfrac{v_0$ \sin \theta}{g}\$$right)^2$$ + \dfrac{2h}{g}}$$

Question 1

A tennis player standing 12.6 m from the net hits the ball at $$3.00^\circ$$ above the horizontal. To just clear the net, the ball must rise at least 0.350 m. If the ball just clears the net at the apex of its trajectory, what is the minimum initial speed the player must give the ball? (Assume $$g = 9.8 \ \mathrm{m/s^2$}.)$$

Accepted Answer

$$v_0 = 22.0$$ \ \mathrm{m/s}$$

Question 2

An artillery shell is fired with an initial velocity of $$300 \ \mathrm{m/s} at$$ $$55.0^\circ$$ above the horizontal. It explodes on a mountainside $$42.0 \mathrm{s}$$ after firing. What is the horizontal distance from the firing point to where it explodes? (Assume no air resistance.)

Accepted Answer

$$d = 7.24 \ \mathrm{km}$$

Question 3

An astronaut on a strange planet finds that she can jump a maximum horizontal distance of $$15.0 \ \mathrm{m} if $$her initial speed is $$3.00 \ \mathrm{m/s}. $$What is the free-fall acceleration on this planet?

Accepted Answer

$$g = 0.60 \ \mathrm{m/s^2$}$$

Question 4

A ball is tossed from an upper-story window of a building. The ball is given an initial velocity of $$8.00 \ \mathrm{m/s} at an $$angle of $$20.0^\circ$$ below the horizontal. It strikes the ground $$3.00 \ \mathrm{s}$$ later. How far horizontally from the base of the building does the ball strike the ground?

Accepted Answer

$$x = 22.6 \ \mathrm{m}$$

Question 5

A cannon with a muzzle speed of $$1000 \ \mathrm{m/s} is $$used to start an avalanche on a mountain. The target is on a mountainside $$2000 \ \mathrm{m}$$ horizontally and $$800 \ \mathrm{m}$$ above the cannon. At what angle, above the horizontal, should the cannon be fired?

Accepted Answer

$$	heta = 24.8^\circ$$

Question 6

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Which of the following expressions gives the maximum height $$H$$ reached by the projectile?

Accepted Answer

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

Question 7

If a projectile is launched at an angle $$	heta$$ and lands at the same height from which it was launched, which of the following gives the total time of flight $$T$$?

Accepted Answer

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

Question 8

A ball is thrown horizontally from the top of a $$45.0 \ \mathrm{m}$$ high cliff with a speed of $$10.0 \ \mathrm{m/s}. $$How far from the base of the cliff will the ball land?

Accepted Answer

$$x = 30.2 \ \mathrm{m}$$

Question 9

A soccer player kicks a ball with an initial speed of $$20.0 \ \mathrm{m/s} at an $$angle of $$30.0^\circ$$ above the horizontal. What is the range of the ball? (Assume $$g = 9.8 \ \mathrm{m/s^2$}$$ and the ball lands at the same height it was kicked.)

Accepted Answer

$$R = 40.8 \ \mathrm{m}$$

Question 10

A projectile is launched at $$60.0^\circ$$ with an initial speed of $$50.0 \ \mathrm{m/s}. $$What is the vertical component of its initial velocity?

Accepted Answer

$$v_{0y} = 43.3 \ \mathrm{m/s}$$

Question 11

A ball is thrown with an initial velocity of $$15.0 \ \mathrm{m/s} at an $$angle of $$45.0^\circ$$ above the horizontal from a $$20.0 \ \mathrm{m}$$ high platform. How long does it take to hit the ground? (Assume $$g = 9.8 \ \mathrm{m/s^2$}.)$$

Accepted Answer

$$t = 3.13 \ \mathrm{s}$$

Question 12

Which of the following best explains why the horizontal velocity of a projectile remains constant (neglecting air resistance)?

Accepted Answer

There is no horizontal force acting on the projectile.

Question 13

A stone is thrown upward at $$20.0 \ \mathrm{m/s}$$ from the edge of a $$50.0 \ \mathrm{m}$$ high cliff. How long does it take to reach the ground?

Accepted Answer

$$t = 6.19 \ \mathrm{s}$$

Question 14

A projectile is launched from the ground at an angle $$	heta$$ with initial speed $$v_0. $$Which launch angle gives the maximum range?

Accepted Answer

$$45.0^\circ$$

Question 15

A ball is thrown at $$10.0 \ \mathrm{m/s} at an $$angle of $$37.0^\circ$$ above the horizontal. What is the time to reach the maximum height?

Accepted Answer

$$t = 0.61 \ \mathrm{s}$$

Question 16

A projectile is launched from a height $$h$$ above the ground with initial speed $$v_0 at an $$angle $$	heta. $$Which equation gives the total time of flight?

Accepted Answer

$$t = \dfrac{v_0$ \sin 	heta}{g} + \sqrt{\left(\dfrac{v_0$ \sin 	heta}{g}\$$right)^2$$ + \dfrac{2h}{g}}$$

Projectile Motion and Two-Dimensional Kinematics: Homework Study Guide

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