Q: A vector $$\vec{A}$$ has components $$A_x = -3$$ and $$A_y = 1. $$What is the direction of $$\vec{A}$$ relative to the positive x-axis?

$$\tan$$^{-1}$$(1/3)$$ above -x$

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$Which combination of $$v_0$$ and $$\theta$$ will maximize the range (neglecting air resistance)?

$$v_0$$ large, $$\theta = 45^\circ$$

Question 1

A soccer ball is kicked straight up and takes 2.0 s to reach its highest point. What was the ball's initial velocity when it left the player's foot? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ and ignore air resistance.)

Accepted Answer

$$10\ \mathrm{m/s}$$

Question 2

Which of the following statements about vectors is TRUE?

Accepted Answer

Multiplying a vector by $$-1$$ reverses its direction but keeps its magnitude the same.

Question 3

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

Accepted Answer

$$5\ \mathrm{km}$$

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

Accepted Answer

$$26\ \mathrm{m}$$

Question 6

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

Accepted Answer

$$g \sin 	heta$$

Question 7

A projectile is launched with an initial velocity $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the initial vertical component of the velocity?

Accepted Answer

$$v_0$$ \sin 	heta$$

Question 8

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

Accepted Answer

2.0 m

Question 9

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

Accepted Answer

Yes

Question 10

A mouse runs straight across a conveyor belt moving at $$3\ \mathrm{m/s}$$ while the mouse runs 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 $$500\ \mathrm{mph}$$ while 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 projectile is launched horizontally from a $$0.61\ \mathrm{m}$$ high dock at $$8.5\ \mathrm{m/s}. $$How far from the dock does it land? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$3.0\ \mathrm{m}$$

Question 13

A vector $$\vec{A}$$ has components $$A_x = -3$$ and $$A_y = 1. $$What is the direction of $$\vec{A}$$ relative to the positive x-axis?

Accepted Answer

$$	an$$^{-1}$$(1/3)$$ above -x$

Question 14

Which of the following best describes the acceleration of an object in uniform circular motion?

Accepted Answer

It points toward the center of the circle.

Question 15

A world-class speed skater rounds a turn of radius $$11\ \mathrm{m} at a $$speed of $$25\ \mathrm{m/s}. $$What is the magnitude of her centripetal acceleration?

Accepted Answer

$$56.8\ \mathrm{m/s^2$}$$

Question 16

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$Which combination of $$v_0$$ and $$	heta$$ will maximize the range (neglecting air resistance)?

Accepted Answer

$$v_0$$ large, $$	heta = 45^\circ$$

Question 17

Which of the following is NOT a property of a vector?

Accepted Answer

Its magnitude can be negative.

Question 18

A kayaker paddles off a waterfall and travels $$0.8\ \mathrm{m} at an $$angle of $$45^\circ$$ below the horizontal in $$0.1\ \mathrm{s}. $$What is the magnitude of the kayaker's velocity during this interval?

Accepted Answer

$$8.0\ \mathrm{m/s}$$

Vectors and Motion in Two Dimensions: Study Guide

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