Q: A projectile is launched with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the time of flight if it lands at the same vertical level from which it was launched? (Neglect air resistance.)

$$t = \dfrac{2v_0 \sin\theta}{g}$$

Q: A vector $$\vec{A}$$ has components $$A_x = -2$$ and $$A_y = 3. $$What is the angle $$\theta ($$measured from the positive x-axis) of $$\vec{A}$$?

$$\theta = 180^\circ + \tan$$^{-1}$$(3/(-2))$$

Question 1

A soccer player kicks a ball straight up into the air, and it takes 2.0 s to reach its highest point. What was the ball's initial velocity when it left the player's foot? (Assume $$g = 10\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$20\ \mathrm{m/s}$$

Question 2

Which of the following statements about vectors is correct?

Accepted Answer

The magnitude of a vector is always a positive quantity.

Question 3

A hiker walks 4 miles east and then 3 miles north. What is the magnitude of the net displacement?

Accepted Answer

$$5\ \mathrm{mi}$$

Question 4

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 5

A crate slides down a frictionless ramp inclined at an angle $$	heta to $$the horizontal. What is the acceleration of the crate parallel to the ramp?

Accepted Answer

$$a = g\sin	heta$$

Question 6

A projectile is launched with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the time of flight if it lands at the same vertical level from which it was launched? (Neglect air resistance.)

Accepted Answer

$$t = \dfrac{2v_0 \sin	heta}{g}$$

Question 7

A car travels around a circular track of radius $$r at $$constant speed $$v. $$What is the direction of its acceleration?

Accepted Answer

Toward the center of the circle.

Question 8

A ball is thrown horizontally from a table and lands 2.0 m from the base. If a second ball with twice the mass is thrown with the same speed, how far from the base will it land?

Accepted Answer

2.0 m

Question 9

A toy car moves around a circular track at constant speed. If the speed doubles, by what factor does the centripetal acceleration change?

Accepted Answer

$$4$$

Question 10

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 11

A plane flies due east at $$500\ \mathrm{mph}$$ relative to the air. The wind blows due south at $$100\ \mathrm{mph}. $$What is the plane’s speed relative to the ground?

Accepted Answer

$$510\ \mathrm{mph}$$

Question 12

A dog runs off a dock horizontally at $$8.5\ \mathrm{m/s}$$ from a height of $$0.61\ \mathrm{m}. $$How far from the dock does the dog land? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$3.0\ \mathrm{m}$$

Question 13

A vector $$\vec{A}$$ has components $$A_x = -2$$ and $$A_y = 3. $$What is the angle $$	heta ($$measured from the positive x-axis) of $$\vec{A}$$?

Accepted Answer

$$	heta = 180^\circ + 	an$$^{-1}$$(3/(-2))$$

Question 14

A skydiver falls at $$35\ \mathrm{m/s}$$ vertically while a wind blows at $$7\ \mathrm{m/s} to $$the west. What is the magnitude of the skydiver’s velocity relative to the ground?

Accepted Answer

$$36\ \mathrm{m/s}$$

Question 15

A car drives up a $$10^\circ$$ slope at $$15\ \mathrm{m/s}$$ for $$10\ \mathrm{s}. $$How much height does the car gain?

Accepted Answer

$$26\ \mathrm{m}$$

Question 16

Which of the following best describes the acceleration of a particle in projectile motion (neglecting air resistance)?

Accepted Answer

It is directed downward at all times.

Question 17

A grasshopper jumps $$0.76\ \mathrm{m} at $$the optimal angle for maximum range. What is the initial speed of the jump? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$2.7\ \mathrm{m/s}$$

Chapter 3: Vectors and Motion in Two Dimensions – Study Notes

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