Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the maximum height reached by the projectile?

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

Question 1

A car travels 670,616,629 miles in 1 year. What is its average speed in meters per second? (1 mile = 1,609.3 m, 1 year = 365 days)

Accepted Answer

$$3.00 	imes 10^4$ m/s

Question 2

An object moves along the x-axis from $$x_i = 8 m to$$ $$x_f = 4 m. $$What is its displacement?

Accepted Answer

$$-4 m$$

Question 3

A ball is thrown vertically upward with a speed of $$29.0 m/s. $$What is its velocity after $$2.96 s$$? (Assume $$g = 9.8 m/s$^2$$ downward)

Accepted Answer

$$-1.33 m/s$

Question 4

A sailor in a small sailboat encounters shifting winds. She sails $$2.00 km $$east, $$3.50 km $$southeast, and then an additional distance in an unknown direction. If her total displacement is $$5.20 km $$directly east of her starting point, what is the magnitude and direction of the third leg?

Accepted Answer

$$2.81 km$$, $$23.8^\circ$$ East of North

Question 5

A ball with a horizontal speed of $$1.25 m/s $$rolls off a bench $$1.00 m $$above the floor. How long will it take the ball to hit the floor? (Assume $$g = 9.8 m/s$^2)$$

Accepted Answer

$$0.452 s$$

Question 6

A skateboarder shoots off a ramp with a velocity of $$6.6 m/s at an $$angle of $$55^\circ$$ above the horizontal. The end of the ramp is $$1.2 m $$above the ground. What is the maximum height above the ground the skateboarder reaches?

Accepted Answer

$$2.0 m$$

Question 7

A car has a mass of $$1500 kg. If $$the driver applies the brakes while going $$9.4 m/s$$, and the maximum friction force the tires can provide without skidding is $$9800 N$$, what is the shortest distance in which the car can stop safely?

Accepted Answer

$$7.2 m$$

Question 8

Two skaters, a man and a woman, are standing on ice. Keegan exerts a force of $$48 N on $$the woman. The mass of the man is $$65 kg $$and the mass of the woman is $$50 kg. $$What is the acceleration of the woman?

Accepted Answer

$$0.96 m/s$^2$$ due West

Question 9

A drag boat is being dragged across the floor at a constant speed by a rope pulling horizontally on it. Which of the following free-body diagrams best represents the forces acting on the boat?

Accepted Answer

A diagram with equal and opposite horizontal forces, and equal and opposite vertical forces

Question 10

A ball is launched from a cannon aimed $$45^\circ$$ above the horizontal. Drag cannot be neglected. Which statement is true about the ball's trajectory?

Accepted Answer

The ball will land closer than it would if drag were neglected

Question 11

A ball is thrown vertically upward with an initial velocity $$v_0. $$What is the velocity of the ball when it returns to the same height from which it was thrown? (Neglect air resistance)

Accepted Answer

$$-v_0$

Question 12

A car skidding to a stop down a $$20^\circ$$ hill is acted on by gravity, friction, and the normal force. Which direction does the friction force act?

Accepted Answer

Up the hill, opposite to the direction of motion

Question 13

A ball is dropped from a height $$h$$ and takes $$t$$ seconds to hit the ground. What is the initial velocity of the ball?

Accepted Answer

$$0$$

Question 14

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the maximum height reached by the projectile?

Accepted Answer

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

Question 15

A ball is thrown horizontally from a $$1.00 m $$high bench with a speed of $$1.25 m/s. $$What is the horizontal distance traveled before hitting the ground?

Accepted Answer

$$0.565 m$$

Question 16

A car accelerates from rest at $$2.0 m/s$^2$$ for $$5.0 s. $$What is its final velocity?

Accepted Answer

$$10.0 m/s$$

Question 17

A ball is thrown upward with velocity $$v_0. $$What is the time to reach the maximum height?

Accepted Answer

$$\dfrac{v_0$}{g}$$

Question 18

A $$1500 kg $$car moving at $$9.4 m/s $$comes to a stop due to friction. What is the work done by friction?

Accepted Answer

$$-66,390 J$$

Question 19

A ball is thrown at $$45^\circ$$ above the horizontal with initial speed $$v_0. $$What is the range of the projectile?

Accepted Answer

$$\dfrac{v_0$^2}{g}$$

Kinematics and Dynamics: Review Problems and Solutions (Chapters 1–4)

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