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

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

Q: A Ferris wheel has a radius of $$9.0\ \mathrm{m}$$ and rotates at $$2.0$$ revolutions per minute. What is the speed of a rider on the edge?

$$v = \dfrac{2\pi \times 9.0}{60} \times 2.0$$

Question 1

A particle moves along a curved path in the xy-plane. Which of the following best describes the direction of its instantaneous velocity vector at any point along the trajectory?

Accepted Answer

It is tangent to the trajectory at that point.

Question 2

A ball is launched horizontally from a cliff of height $$h$$ with initial speed $$v_0. At $$the same instant, another ball is dropped from the same height. Neglecting air resistance, which statement is true about the time it takes for each ball to hit the ground?

Accepted Answer

Both balls hit the ground at the same time.

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-m-high cliff with a horizontal speed of $$20.0\ \mathrm{m/s}. $$How far from the base of the cliff does the car land? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$28.6\ \mathrm{m}$$

Question 5

Which equation gives the magnitude of the centripetal acceleration for a particle moving in a circle of radius $$r at $$speed $$v$$?

Accepted Answer

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

Question 6

A wheel rotates at a constant angular velocity $$\omega. $$What is the period $$T of $$the motion?

Accepted Answer

$$T = \dfrac{2\pi}{\omega}$$

Question 7

A Ferris wheel has a radius of $$9.0\ \mathrm{m}$$ and rotates at $$2.0$$ revolutions per minute. What is the speed of a rider on the edge?

Accepted Answer

$$v = \dfrac{2\pi 	imes 9.0}{60} 	imes 2.0$$

Question 8

A ball moves in a circle of radius $$r$$ with constant speed $$v. $$Which statement is true about its acceleration?

Accepted Answer

The acceleration points toward the center of the circle.

Question 9

A hunter aims directly at a coconut hanging from a tree. At the instant the arrow is released, the coconut falls. Neglecting air resistance, what happens?

Accepted Answer

The arrow hits the coconut.

Question 10

A particle moves from position $$\vec{r}_1 to$$ $$\vec{r}_2 in $$time $$\Delta t. $$What is the formula for its average velocity?

Accepted Answer

$$\vec{v}_{avg} = \dfrac{\vec{r}_2 - \vec{r}_1}{\Delta t}$$

Question 11

A wheel starts from rest and undergoes constant angular acceleration, turning through $$25\ \mathrm{rad} in $$time $$t. $$How many radians will it have turned after time $$2t$$?

Accepted Answer

$$100\ \mathrm{rad}$$

Question 12

A ball rolls off a table and lands $$2.0\ \mathrm{m}$$ from the base. A second ball, twice as massive, rolls off with the same speed. Where does it land?

Accepted Answer

Between $$2\ \mathrm{m}$$ and $$4\ \mathrm{m}$$

Question 13

Which of the following is true about the independence of horizontal and vertical motions in projectile motion?

Accepted Answer

The horizontal and vertical motions are independent, but share the same time of flight.

Question 14

A particle moves in a circle of radius $$r$$ with angular velocity $$\omega. $$What is its tangential speed?

Accepted Answer

$$v = \omega r$$

Question 15

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

Accepted Answer

Twice as much

Question 16

Sofia and Rasheed are riding a merry-go-round spinning steadily. 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 17

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 18

Which of the following best describes the direction of the acceleration vector for a particle in uniform circular motion?

Accepted Answer

Toward the center of the circle

Kinematics in Two Dimensions: Study Notes

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