Q: A projectile is launched with initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What are the initial velocity components?

$$v_{0x} = v_0$ \cos \theta$$, $$v_{0y} = v_0$ \sin \theta$$

Question 1

A particle moves from position $$\vec{r}_1 at $$time $$t_1 to $$position $$\vec{r}_2 at $$time $$t_2. $$Which equation correctly expresses the average velocity vector $$\vec{v}_{avg}$$?

Accepted Answer

$$\vec{v}_{avg} = \frac{\vec{r}_2 - \vec{r}_1}{t_2$ - t_1$}$$

Question 2

Which statement best describes the direction of the instantaneous velocity vector for a particle moving along a curved path?

Accepted Answer

It is tangent to the trajectory at the particle's position.

Question 3

A projectile is launched with initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What are the initial velocity components?

Accepted Answer

$$v_{0x} = v_0$ \cos 	heta$$, $$v_{0y} = v_0$ \sin 	heta$$

Question 4

A car drives off a $$10.0\ \mathrm{m}$$ high cliff with a horizontal speed of $$20.0\ \mathrm{m/s}. $$Neglecting air resistance, how far from the base of the cliff does the car land?

Accepted Answer

$$28.6\ \mathrm{m}$$

Question 5

Two balls are released from the same height above the ground at the same instant. One is dropped vertically, and the other is launched horizontally. Neglecting air resistance, which hits the ground first?

Accepted Answer

They hit the ground at the same time.

Question 6

A hunter aims directly at a coconut hanging from a tree. At the instant the arrow is released, the coconut falls. Will the arrow hit the coconut?

Accepted Answer

Yes, the arrow will hit the coconut.

Question 7

For projectile motion over level ground, what launch angle $$	heta$$ gives the maximum range?

Accepted Answer

$$45^\circ$$

Question 8

A mouse runs straight across a conveyor belt moving at $$3\ \mathrm{m/s}$$, heading for cheese at $$4\ \mathrm{m/s}$$ relative to the belt. What is the mouse’s speed relative to the factory floor?

Accepted Answer

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

Question 9

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

Accepted Answer

$$502.5\ \mathrm{mph}$$

Question 10

A ball moves in uniform circular motion with radius $$r$$ and speed $$v. $$What is the magnitude of its centripetal acceleration?

Accepted Answer

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

Question 11

Sofia and Rasheed are riding a spinning merry-go-round. Sofia is twice as far from the axis as Rasheed. How does Sofia’s tangential velocity compare to Rasheed’s?

Accepted Answer

Twice as much

Question 12

Sofia and Rasheed are riding a spinning merry-go-round. Sofia is twice as far from the axis as Rasheed. How does Sofia’s centripetal acceleration compare to Rasheed’s?

Accepted Answer

Four times as much

Question 13

A car is traveling around a circular track at a steady $$45\ \mathrm{mph}. Is $$the car accelerating?

Accepted Answer

Yes, because the direction of velocity is changing.

Question 14

A ball moves in a circle of radius $$r$$ with constant angular velocity $$\omega. $$What is the relationship between its tangential speed $$v$$ and $$\omega$$?

Accepted Answer

$$v = \omega r$$

Question 15

Which of the following is true about the independence of horizontal and vertical motion in projectile motion (neglecting air resistance)?

Accepted Answer

The time to reach the ground depends only on the vertical motion.

Question 16

A particle moves in two dimensions with velocity components $$v_x$$ and $$v_y. $$What is the speed of the particle?

Accepted Answer

$$v = \sqrt{v_x^2$ + v_y^2$}$$

Question 17

A ball on a roulette wheel of diameter $$1.0\ \mathrm{m}$$ completes $$2.0$$ revolutions in $$20.0\ \mathrm{s}. $$What is its angular velocity?

Accepted Answer

$$0.628\ \mathrm{rad/s}$$

Question 18

A pilot wants to fly due east from Chicago to Cleveland, but there is a south wind. To reach Cleveland directly, in which direction should the pilot point the plane?

Accepted Answer

North of east

Kinematics in Two Dimensions – Study Notes

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