Q: A projectile is launched from the ground with speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the formula for the range $$R ($$horizontal distance traveled) over level ground?

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

Question 1

A soccer ball is kicked from ground level with an initial speed of 20 m/s at an angle of 30° above the horizontal. Neglecting air resistance, what is the maximum height the ball reaches? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$5.1\ \mathrm{m}$$

Question 2

A car drives off a horizontal 15 m high bridge at 25 m/s. How far from the base of the bridge does the car land? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$61\ \mathrm{m}$$

Question 3

A projectile is launched from the ground with speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the formula for the range $$R ($$horizontal distance traveled) over level ground?

Accepted Answer

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

Question 4

A 0.5 kg ball and a 2 kg ball are both rolled off the same table with the same horizontal speed. Which statement is true about their landing distances (neglecting air resistance)?

Accepted Answer

Both balls land at the same distance from the table.

Question 5

A plane flies due east at 200 m/s relative to the air. The wind blows due north at 50 m/s. What is the plane’s speed relative to the ground?

Accepted Answer

$$223.6\ \mathrm{m/s}$$

Question 6

A merry-go-round spins at a constant angular velocity $$\omega. $$Two children, Alice and Bob, sit at radii $$r$$ and $$2r$$ from the center, respectively. Which statement is correct about their speeds?

Accepted Answer

Bob’s speed is twice Alice’s speed.

Question 7

A wheel starts from rest and accelerates with a constant angular acceleration $$\alpha. $$After time $$t$$, it has turned through an angle $$	heta. $$How far will it have turned after time $$2t$$?

Accepted Answer

$$4	heta$$

Question 8

A car travels around a circular track of radius 50 m at a constant speed of 20 m/s. What is the magnitude of its centripetal acceleration?

Accepted Answer

$$8\ \mathrm{m/s^2$}$$

Question 9

A fan blade is spinning counterclockwise and slowing down. What are the signs of its angular velocity $$\omega$$ and angular acceleration $$\alpha$$?

Accepted Answer

$$\omega is $$positive and $$\alpha is $$negative.

Question 10

A mouse runs directly across a conveyor belt moving at 3 m/s. The mouse’s speed relative to the belt is 4 m/s. What is the mouse’s speed relative to the ground?

Accepted Answer

$$5\ \mathrm{m/s}$$

Question 11

A ball is thrown upward at a 45° angle. In the absence of air resistance, what is the shape of its trajectory?

Accepted Answer

A parabolic curve

Question 12

A bullet is fired directly at a coconut hanging from a tree. At the instant the bullet is fired, the coconut falls. Neglecting air resistance, what happens?

Accepted Answer

The bullet hits the coconut.

Question 13

A 0.2 kg ball rolls off a table and lands 2.0 m from the base. If a 0.4 kg ball rolls off the same table with the same speed, how far does it land from the base?

Accepted Answer

2.0 m

Question 14

A wheel rotates at a constant angular velocity $$\omega = 2\ \mathrm{rad/s}. $$What is the period $$T of $$the motion?

Accepted Answer

$$\pi\ \mathrm{s}$$

Question 15

A ball moves in a circle of radius $$r$$ with constant speed $$v. $$What is the direction of its acceleration?

Accepted Answer

Toward the center of the circle

Question 16

A wheel starts from rest and reaches an angular velocity of $$30\ \mathrm{rad/s} in 5 s $$with constant angular acceleration. What is the angular acceleration?

Accepted Answer

$$3\ \mathrm{$$rad/s^2$$}$$

Question 17

A Ferris wheel has a radius of 10 m and completes one revolution every 20 s. What is the speed of a rider?

Accepted Answer

$$1.57\ \mathrm{m/s}$$

Question 18

A particle moves in a circle of radius $$r$$ with angular velocity $$\omega. $$What is the formula for its centripetal acceleration?

Accepted Answer

$$a_c = \$$omega^2$$ r$$

Question 19

A wheel spinning at 60 rpm comes to rest in 30 s with constant angular acceleration. How many revolutions does it make while stopping?

Accepted Answer

Kinematics in Two Dimensions: Motion, Projectile Motion, and Circular Motion

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