Q: A hockey puck slides across a frictionless air table at a velocity of $$2.0\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the x-axis. What is the y-component of its velocity?

$$v_y = 2.0\ \mathrm{m/s} \times \sin(30^\circ) = 1.0\ \mathrm{m/s}$$

Q: A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. Which equation gives the maximum height $$h_{max}$$ reached by the projectile (ignoring air resistance)?

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

Q: A projectile is fired from a cannon at a $$30^\circ$$ angle with an initial velocity of $$100\ \mathrm{m/s}. $$How long will the projectile spend in the air? (Assume $$g = 9.81\ \mathrm{m/s^2$}$$ and it lands at the same height it was launched.)

$$t = \dfrac{2 v_0$ \sin \theta}{g} = \dfrac{2 \times 100 \times \sin 30^\circ}{9.81} \approx 10.2\ \mathrm{s}$$

Q: A car makes 4.0 laps around a circular racetrack of radius $$50.0\ \mathrm{m} in$$ $$5.0\ \mathrm{min}. $$What is the car's average angular speed in $$\mathrm{rad/s}$$?

$$\omega = \dfrac{4 \times 2\pi}{300} = 0.084\ \mathrm{rad/s}$$

Q: A record accelerates from rest to $$33\frac{1}{3}$$ rpm in $$5.00\ \mathrm{s}. $$What is its angular acceleration in $$\mathrm{$$rad/s^2$$}$$?

$$\alpha = \dfrac{\omega_f - \omega_i}{t} = \dfrac{(33.33 \times \dfrac{2\pi}{60}) - 0}{5.00} \approx 0.70\ \mathrm{$$rad/s^2$$}$$

Q: A merry-go-round has a radius of $$2.00\ \mathrm{m}$$ and rotates at $$1.00\ \mathrm{rev/s}. $$What is the tangential speed of a child sitting at the edge?

$$v = 2\pi r f = 2\pi \times 2.00 \times 1.00 = 12.57\ \mathrm{m/s}$$

Question 1

A hockey puck slides across a frictionless air table at a velocity of $$2.0\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the x-axis. What is the y-component of its velocity?

Accepted Answer

$$v_y = 2.0\ \mathrm{m/s} 	imes \sin(30^\circ) = 1.0\ \mathrm{m/s}$$

Question 2

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Which equation gives the maximum height $$h_{max}$$ reached by the projectile (ignoring air resistance)?

Accepted Answer

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

Question 3

A ball is thrown straight up from the edge of a cliff with an initial speed of $$20.0\ \mathrm{m/s}. $$Another ball is thrown straight down with the same speed from the same height. Neglecting air resistance, which ball has the greater speed when it hits the ground?

Accepted Answer

Both have the same speed

Question 4

A hockey puck on an air table starts at rest and receives a constant acceleration $$\vec{a} = 10\left(\dfrac{m}{s^2$}\right)\hat{x} + 20\left(\dfrac{m}{s^2$}\right)\hat{y}. $$What is the magnitude of its velocity after $$0.10\ \mathrm{s}$$?

Accepted Answer

$$v = \sqrt{(1.0)^2$ + (2.0)^2$} = 2.24\ \mathrm{m/s}$$

Question 5

A projectile is fired from a cannon at a $$30^\circ$$ angle with an initial velocity of $$100\ \mathrm{m/s}. $$How long will the projectile spend in the air? (Assume $$g = 9.81\ \mathrm{m/s^2$}$$ and it lands at the same height it was launched.)

Accepted Answer

$$t = \dfrac{2 v_0$ \sin 	heta}{g} = \dfrac{2 	imes 100 	imes \sin 30^\circ}{9.81} \approx 10.2\ \mathrm{s}$$

Question 6

Which of the following statements about projectile motion is correct (ignoring air resistance)?

Accepted Answer

The horizontal velocity remains constant throughout the flight.

Question 7

A car makes 4.0 laps around a circular racetrack of radius $$50.0\ \mathrm{m} in$$ $$5.0\ \mathrm{min}. $$What is the car's average angular speed in $$\mathrm{rad/s}$$?

Accepted Answer

$$\omega = \dfrac{4 	imes 2\pi}{300} = 0.084\ \mathrm{rad/s}$$

Question 8

A record accelerates from rest to $$33\frac{1}{3}$$ rpm in $$5.00\ \mathrm{s}. $$What is its angular acceleration in $$\mathrm{$$rad/s^2$$}$$?

Accepted Answer

$$\alpha = \dfrac{\omega_f - \omega_i}{t} = \dfrac{(33.33 	imes \dfrac{2\pi}{60}) - 0}{5.00} \approx 0.70\ \mathrm{$$rad/s^2$$}$$

Question 9

A coin sits at the edge of a rotating disk of radius $$r. If $$the disk rotates at angular speed $$\omega$$, what is the tangential speed $$v of $$the coin?

Accepted Answer

$$v = \omega r$$

Question 10

A stick rotates about a fixed pole. Five people hold the stick at different distances from the pole. Who moves fastest?

Accepted Answer

The person farthest from the pole

Question 11

A merry-go-round has a radius of $$2.00\ \mathrm{m}$$ and rotates at $$1.00\ \mathrm{rev/s}. $$What is the tangential speed of a child sitting at the edge?

Accepted Answer

$$v = 2\pi r f = 2\pi 	imes 2.00 	imes 1.00 = 12.57\ \mathrm{m/s}$$

Question 12

What is the centripetal acceleration $$a_c of an $$object moving at speed $$v in a $$circle of radius $$r$$?

Accepted Answer

$$a_c = \dfrac{v^2$}{r}$$

Question 13

A battleship fires two shells at enemy ships A and B. If both shells are fired simultaneously and follow parabolic trajectories, which ship is hit first?

Accepted Answer

Ship A (closer target)

Question 14

A key is hanging from a tree and you want to hit it with a rock. If the monkey drops at the same time as you throw, where should you aim?

Accepted Answer

Directly at the monkey

Question 15

A disk rotates at a constant angular speed $$\omega. $$What is the direction of the centripetal acceleration for a point on the edge of the disk?

Accepted Answer

Radially inward toward the center

Question 16

A record player accelerates from rest to $$33\frac{1}{3}$$ rpm in $$5.00\ \mathrm{s}$$, then is stopped in $$0.50\ \mathrm{s}. $$Which has the greater magnitude of angular acceleration?

Accepted Answer

Stopping acceleration

Question 17

A ball is dropped from a height and another is launched horizontally from the same height. Which hits the ground first (neglecting air resistance)?

Accepted Answer

Both hit at the same time

Question 18

A circular track has a radius of $$50.0\ \mathrm{m}. If $$you walk $$2.00$$ miles, how many times around the track is this? ($$1\ \mathrm{mile} = 1609\ \mathrm{m})$$

Accepted Answer

$$\dfrac{2.00 	imes 1609}{2\pi 	imes 50.0} \approx 10.25$$ revolutions

Kinematics in Two Dimensions: Kinematics, Projectile Motion, and Angular Motion (Physics 130, Lecture 4)

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