Q: A ball is launched with an initial velocity $$\vec{v}_0 at an $$angle $$\theta$$ above the horizontal. What are the correct expressions for the initial velocity components?

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

Q: A projectile is launched with speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the equation for its vertical position $$y as a $$function of time $$t ($$assuming $$y_0 = 0$)?

$$y = v_0$ \sin \theta\ t - \frac{1}{2}gt^2$

Q: A particle moves in the x-y plane with velocity components $$v_x$$ and $$v_y. $$What is the direction $$\theta of $$the velocity vector with respect to the x-axis?

$$\theta = \tan$$^{-1}$$(v_y / v_x)$$

Question 1

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

Accepted Answer

It is tangent to the trajectory at that point.

Question 2

A ball is launched with an initial velocity $$\vec{v}_0 at an $$angle $$	heta$$ above the horizontal. What are the correct expressions for the initial velocity components?

Accepted Answer

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

Question 3

A car drives off a 10 m high cliff with a horizontal speed of 20 m/s. Neglecting air resistance, 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 4

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

Accepted Answer

The horizontal and vertical motions are independent except for sharing the same time interval.

Question 5

A ball is thrown horizontally from a height $$h$$ and another is dropped from the same height at the same instant. Which hits the ground first?

Accepted Answer

They hit at the same time.

Question 6

A particle moves in a circle of radius $$r at $$constant speed $$v. $$What is the magnitude of its acceleration?

Accepted Answer

$$a = v^2$/r$$

Question 7

A Ferris wheel has a radius of $$9.0\ \mathrm{m}$$ and rotates twice per minute. What is the speed of a rider? (Use $$\pi \approx 3.14)$$

Accepted Answer

$$1.88\ \mathrm{m/s}$$

Question 8

A ball rolls around a circular track with an angular velocity of $$4\pi\ \mathrm{rad/s}. $$What is the period of the motion?

Accepted Answer

$$0.5\ \mathrm{s}$$

Question 9

A wheel with constant angular acceleration turns through an angle of $$25\ \mathrm{rad} in $$time $$t$$, starting from rest. Through what angle will it have turned after time $$2t$$?

Accepted Answer

$$75\ \mathrm{rad}$$

Question 10

A projectile is launched with speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the equation for its vertical position $$y as a $$function of time $$t ($$assuming $$y_0 = 0$)?

Accepted Answer

$$y = v_0$ \sin 	heta\ t - \frac{1}{2}gt^2$

Question 11

A 100 g ball rolls off a table and lands 2.0 m from the base. A 200 g ball rolls off the same table with the same speed. Where does it land?

Accepted Answer

2.0 m

Question 12

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

Accepted Answer

$$v_t = \omega r$$

Question 13

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

Accepted Answer

Yes, because its direction is changing.

Question 14

A particle moves in the x-y plane with velocity components $$v_x$$ and $$v_y. $$What is the direction $$	heta of $$the velocity vector with respect to the x-axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$(v_y / v_x)$$

Question 15

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 16

In the same scenario, Sofia's speed is ______ that of Rasheed.

Accepted Answer

Twice

Question 17

In the same scenario, Sofia's centripetal acceleration is ______ that of Rasheed.

Accepted Answer

Four times

Question 18

A particle moves in a circle of radius $$r$$ with constant speed $$v. $$What is the direction of its acceleration?

Accepted Answer

Toward the center of the circle

Question 19

A hungry 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.

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

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