Q: A projectile is launched from the ground with initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the range (horizontal distance traveled) before it returns to the ground?

$$\frac{v_0$^2 \sin(2\theta)}{g}$$

Question 1

A projectile is launched with an initial speed $$v_i at an $$angle $$	heta$$ above the horizontal. What is the correct expression for the horizontal component of the initial velocity?

Accepted Answer

$$v_i \cos(	heta)$$

Question 2

A ball is thrown horizontally from the top of a 45 m high cliff with an initial speed of 15 m/s. How long does it take to reach the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.5\ \mathrm{s}$$

Question 3

Which of the following best describes the acceleration vector of a particle in projectile motion (neglecting air resistance)?

Accepted Answer

It is directed downward at all times.

Question 4

A hunter aims directly at a coconut hanging from a tree. At the instant the hunter fires, the coconut begins to fall. What happens?

Accepted Answer

The bullet hits the coconut.

Question 5

A car is traveling around a circular track at constant speed. What is the direction of its acceleration?

Accepted Answer

Toward the center of the circle.

Question 6

A 100 g ball and a 200 g ball roll off the same table with the same speed. The 200 g ball lands at what distance compared to the 100 g ball?

Accepted Answer

The same distance.

Question 7

A plane flies due east at 500 mph. The wind blows due south at 100 mph. What is the magnitude of the plane’s velocity relative to the ground?

Accepted Answer

$$\sqrt{500^2$ + 100^2$}\ \mathrm{mph}$$

Question 8

A ball is launched at an angle $$	heta$$ with initial speed $$v_i. $$What is the time to reach maximum height?

Accepted Answer

$$\frac{v_i \sin(	heta)}{g}$$

Question 9

A car is slowing down as it drives over a circular hill. At the highest point, what is the direction of the acceleration vector?

Accepted Answer

Downward and toward the center of the circle.

Question 10

A wheel starts from rest and has a constant angular acceleration. If it turns through an angle $$	heta in $$time $$t$$, how much will it have turned after time $$2t$$?

Accepted Answer

$$4	heta$$

Question 11

A boat can move at 6.1 m/s in still water. If it points 25° upstream on a river flowing at 1.4 m/s, what is the boat’s velocity relative to the ground?

Accepted Answer

The vector sum of 6.1 m/s at 25° upstream and 1.4 m/s downstream.

Question 12

If the velocity vector of a projectile makes an angle $$	heta$$ with the vertical axis, what is the x-component of the velocity?

Accepted Answer

$$-v \cos(	heta)$$

Question 13

A car is traveling around a curve at a steady 45 mph. Is the car accelerating?

Accepted Answer

Yes, because the direction of velocity is changing.

Question 14

A merry-go-round spins at a constant rate. Sofia is twice as far from the axis as Rasheed. Compared to Rasheed, Sofia’s angular velocity is:

Accepted Answer

The same.

Question 15

A fan blade is slowing down. What are the signs of $$\omega ($$angular velocity) and $$\alpha ($$angular acceleration) if $$\omega is $$positive?

Accepted Answer

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

Question 16

A projectile is launched from the ground with initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the range (horizontal distance traveled) before it returns to the ground?

Accepted Answer

$$\frac{v_0$^2 \sin(2	heta)}{g}$$

Question 17

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

Accepted Answer

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

Question 18

A seagull flies at 10 m/s north relative to the air. The wind blows at 2 m/s south relative to the ground. How long will it take the seagull to travel 4000 m north relative to the ground?

Accepted Answer

$$333\ \mathrm{s}$$

Question 19

If $$	heta = 60^\circ$$, what is $$	heta in $$radians?

Accepted Answer

$$\pi/3$$

Question 20

In uniform circular motion, the magnitude of the centripetal acceleration is given by:

Accepted Answer

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

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

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