Q: Which of the following best describes the trajectory of a projectile launched at an angle $$\theta$$ with initial speed $$v_0 ($$neglecting air resistance)?

A parabolic path described by $$y = x \tan \theta - \frac{gx^2$}{2v_0^2$ \cos^2$ \theta}.$$

Q: A projectile is launched from ground level with speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the formula for the range (horizontal distance) it travels before returning to the same elevation?

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

Q: Which of the following is the correct relationship between angular displacement $$\Delta \theta$$, angular velocity $$\omega$$, and time $$\Delta t$$ for constant angular velocity?

$$\Delta \theta = \omega \Delta t$$

Question 1

A hunter aims directly at a coconut hanging from a tree. At the instant the arrow is released, the coconut begins to fall. Ignoring air resistance, what happens to the arrow?

Accepted Answer

The arrow hits the coconut because both fall the same vertical distance $$\frac{1}{2}gt^2$ during the arrow's flight.

Question 2

Which of the following best describes the trajectory of a projectile launched at an angle $$	heta$$ with initial speed $$v_0 ($$neglecting air resistance)?

Accepted Answer

A parabolic path described by $$y = x 	an 	heta - \frac{gx^2$}{2v_0^2$ \cos^2$ 	heta}.$$

Question 3

A projectile is launched from ground level with speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the formula for the range (horizontal distance) it travels before returning to the same elevation?

Accepted Answer

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

Question 4

A police car moving at $$50\ \mathrm{m/s}$$ fires a bullet forward at $$300\ \mathrm{m/s}$$ relative to the car. What is the bullet's speed relative to a stationary observer on the ground?

Accepted Answer

$$350\ \mathrm{m/s}$$

Question 5

A plane flies due east at $$500\ \mathrm{mph}$$ relative to the air, but there is a $$50\ \mathrm{mph}$$ wind blowing due south. What is the plane's ground speed?

Accepted Answer

$$502\ \mathrm{mph}$$

Question 6

A Ferris wheel has a radius of $$9.0\ \mathrm{m}$$ and rotates $$4.0$$ times per minute. What is the centripetal acceleration experienced by a rider?

Accepted Answer

$$1.6\ \mathrm{m/s}^2$$

Question 7

Which equation correctly relates the tangential velocity $$v_t of a $$particle in uniform circular motion to its angular velocity $$\omega$$ and radius $$r$$?

Accepted Answer

$$v_t = r \omega$$

Question 8

A ceiling fan spinning at $$60\ \mathrm{rpm}$$ coasts to a stop in $$25\ \mathrm{s}. $$How many revolutions does it make while stopping? (Use $$1\ \mathrm{rev} = 2\pi\ \mathrm{rad})$$

Accepted Answer

$$13$$ revolutions

Question 9

Which of the following statements about centripetal acceleration in uniform circular motion is correct?

Accepted Answer

It is always directed toward the center and has magnitude $$a_c = \frac{v^2$}{r}.$$

Question 10

A rotating wheel starts from rest and reaches an angular velocity of $$10\ \mathrm{rad/s} in$$ $$2\ \mathrm{s}$$ with constant angular acceleration. What is the angular acceleration?

Accepted Answer

$$5\ \mathrm{rad/s}^2$$

Question 11

A ball moves in a circle of radius $$0.5\ \mathrm{m} at a $$constant speed of $$2\ \mathrm{m/s}. $$What is its angular velocity?

Accepted Answer

$$4\ \mathrm{rad/s}$$

Question 12

Which of the following is the correct Galilean transformation for velocities?

Accepted Answer

$$v_{CB} = v_{CA} + v_{AB}$$

Question 13

A crankshaft of diameter $$4.0\ \mathrm{cm}$$ rotates at $$2400\ \mathrm{rpm}. $$What is the speed of a point on its surface?

Accepted Answer

$$5.0\ \mathrm{m/s}$$

Question 14

A particle moves in a circle and its angular velocity increases with time. Which of the following is true?

Accepted Answer

The particle has both centripetal and tangential acceleration.

Question 15

A pilot wants to fly directly east from Chicago to Cleveland, but there is a wind blowing south. What heading should the pilot choose?

Accepted Answer

Slightly north of east to compensate for the wind

Question 16

Which of the following is the correct relationship between angular displacement $$\Delta 	heta$$, angular velocity $$\omega$$, and time $$\Delta t$$ for constant angular velocity?

Accepted Answer

$$\Delta 	heta = \omega \Delta t$$

Question 17

If a rotating object slows down in the counterclockwise direction, what are the signs of its angular velocity $$\omega$$ and angular acceleration $$\alpha$$?

Accepted Answer

$$\omega \u003e 0$$, $$\alpha \u003c 0$$

Question 18

A ball on a roulette wheel completes $$2.0$$ revolutions in $$1.20\ \mathrm{s}. $$What is its angular velocity?

Accepted Answer

$$10.47\ \mathrm{rad/s}$$

Kinematics in Two Dimensions: Projectile and Circular Motion

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