chapter 3

Question 1

vectors

Answer 1

quantities that have both a magnitude and direction

ex. displacement, velocity, force, momentum

Question 2

scalars

Answer 2

physical quantities are fully described by a number without a direction

ex. mass, energy, temperature

Question 3

If two vectors are given such that 𝐀 + 𝐁 = 0, what can you say about the
magnitude and direction of vectors 𝐀 and 𝐁 ?

Answer 3

same magnitude, but must be in opposite directions

ex. proven by the tail-to-tip method

Question 4

Given that 𝐀 + 𝐁 = ⃗ 𝐂 and 𝐴 + 𝐵 = 𝐶, how are vectors 𝐀 and 𝐁 oriented with
respect to each other?

Answer 4

they are parallel and in the same direction

Question 5

Vector 𝐀𝐀 has a magnitude of 30 cm at an angle of 30° with the horizontal. Vector 𝐁𝐁 has a magnitude of 20 cm at
an angle of 60° with the horizontal.
(a) Find 𝐴𝑥, A𝑦, 𝐵𝑥, and 𝐵𝑦
b.) Find magnitude and direction of A + B
c.) Find magnitude and direction of A - B
d.) Find magnitude and direction of 2A + 3B

Answer 5

a.) Ax = 26 cm Ay = 15 cm
Bx = 10 cm By = 17 cm

b.) 42°

c.) -8.2°

d.) -45°

Question 6

projectile motion

Answer 6

motion of freely falling objects in 2D

Question 7

Two balls are released from the same height at the same time. One ball is
dropped while the other is thrown horizontally. Which ball hits the ground first?

Answer 7

They will both hit the ground at the same time

Question 8

A battleship simultaneously fires two shells at enemy ships. If the shells follow
the parabolic trajectories shown, which ship gets hit first?

Answer 8

Ship B

(spends less time traveling up and down)

Question 9

A football is kicked at ground level with a speed of
18.0 m/s at an angle of 38.0° to the horizontal. How
much later does it hit the ground?

Answer 9

2.26 seconds

Question 10

Extreme-sports enthusiasts have been known to jump off
the top of El Capitan, a sheer granite cliff of height 910 m
in Yosemite National Park. Assume a jumper runs
horizontally off the top of El Capitan with speed 5.0 m/s
and enjoys a freefall until she is 150 m above the valley
floor, at which time she opens her parachute.

(a) How long
is the jumper in freefall?
(b) How far from the cliff is this
jumper when she opens her chute?

Answer 10

a.) 12 seconds
b.) 62 meters

Question 11

A small cart is rolling at constant velocity on a flat track. While the cart is moving
it fires a ball straight up into the air. A short time after it is fired, what happens to
the ball?

Answer 11

it falls right back into the cart

(both the cart
and the ball have the same horizontal
velocity)

Question 12

Suppose a cannon can launch a soccer ball at 30 m/s. If the cannon is placed
in the back of a truck moving forward at velocity 30 m/s and it fires the soccer
ball horizontally backwards, what is the initial speed of the soccer ball?

Answer 12

0 m/s

Question 13

You are trying to cross a river that flows due south with a strong current. You
start out in your motorboat on the west bank desiring to reach the east bank
directly east from your starting point. You should head your motorboat

Answer 13

northeast direction

Question 14

(a) A person going for a morning jog on the deck of a cruise ship is running
toward the front of the ship at 2.0 m/s while the ship is moving ahead at 8.5 m/s.
What is the velocity of the jogger relative to the water?

(b) Later, the jogger is
moving toward the rear of the ship. What is the jogger’s velocity relative to the
water now?

Answer 14

a.) 2 m/s + 8.5 m/s = 11 m/s

b.) -2.0 m/s +8.5 m/s = 6.5 m/s

Question 15

Huck Finn walks at a speed of 0.70 m/s across his raft. The raft is traveling
down the Mississippi River at a speed of 1.50 m/s relative to the riverbank.
What is Huck’s velocity (speed and direction) relative to the riverbank?

Answer 15

V hbx = 1.50 m/s
V hby = 0.70 m/s

speed = 1.66 m/s
direction = 25° relative to the river

Question 16

An airplane with an airspeed of 120 km/h has a heading of 30°
east of north in a wind that is blowing toward the west at 30 km/h.
What is the speed of the plane relative to the ground?

Answer 16

= around 110 km/hr

Question 17

Which of the following is an example of a vector quantity?

Answer 17

velocity, force, momentum, displacement

Question 18

Which of the following operations will not change a vector?

Answer 18

translate it parallel to itself

Question 19

Two displacement vectors have magnitudes of 5.0 m and 7.0 m, respectively. When these two vectors are added, the magnitude of the sum _______

Answer 19

could be as small as 2.0 m, or as large as 12 m.

Question 20

Determine the resultant vector sum (both magnitude and direction) of the following three vectors.

1. |R1| = 5 and θ1 = 45°
2. |R2| = 10 and θ2 = 90°
3. |R3| = 12 and θ3 = -48.5°

Answer 20

|R| = 12 and θ = 24°

Question 21

Determine the resultant vector sum of the four vectors.

1. |R1| = 5 and θ1 = 45°
2. |R2| = 10 and θ2 = 90°
3. |R3| = 12 and θ3 = 48.5°
4. |R4| = 10 and θ4 = 135°

Answer 21

|R| = 30 at 82°

Question 22

Three force vectors, each having a magnitude of 30 N, pull on an object in directions that are 120° apart from each other. Which of the following statements concerning the magnitude of the resultant force vector is true?

Answer 22

The resultant vector’s magnitude is zero.

Question 23

In the diagram shown above, the unknown vector is ________

Answer 23

A-B

Question 24

Ignoring air resistance, the horizontal component of a projectile’s velocity ________

Answer 24

remains constant

Question 25

Ignoring air resistance, the horizontal component of a projectile’s acceleration _________

Answer 25

is zero

Question 26

If the acceleration of an object is always directed perpendicular to its velocity, _________

Answer 26

the object is turning

Question 27

At what angle should a water-gun be aimed in order for the water to land with the greatest horizontal range?

Answer 27

45°

Question 28

An Olympic athlete throws a javelin at four different angles above the horizontal, each with the same speed: 30°, 40°, 60°, and 80°. Which two throws cause the javelin to land the same distance away?

Answer 28

30° and 60°

Question 29

A package of supplies is dropped from a plane while it is flying, and one second later a second package is dropped. Neglecting air resistance, the horizontal component of distance between the packages will _________ as they are fallin..

Answer 29

be constant

Question 30

Two force vectors are acting on an object as shown in the figure above. What is the magnitude of the resultant force vector?

Answer 30

185 N

Question 31

Two force vectors are acting on an object as shown in the figure above. What is the direction of the resultant force vector?

Answer 31

78° above the +x axis

Question 32

A stone is thrown horizontally with an initial speed of 10 m/s from the edge of a cliff. A stop watch measures the stone’s trajectory time from the top of the cliff to the bottom to be 4.3 s. What is the height of the cliff?

Answer 32

91 m

Question 33

A girl throws a rock horizontally, with a velocity of 10 m/s, from a bridge. It falls 20 m to the water below. How far does the rock travel horizontally before striking the water?

Answer 33

20 m

Question 34

A plane has an air speed of 200 m/s due North, and is in a wind of 50.0 m/s to the West. The plane’s speed relative to the ground is ________

Answer 34

206 m/s

Question 35

The resultant of two vectors is the smallest when the angle between them is _________

Answer 35

180°

Question 36

Two vectors, of magnitudes 20 and 50, are added. Which of the following is a possible answer for the magnitude of the resultant?

Answer 36

40

Question 37

A bullet is fired horizontally, and at the same instant a second bullet is dropped from the same height. Ignore air resistance. Compare the falling times of the two bullets.

Answer 37

They both hit the ground at the same time.

Question 38

A plane flying horizontally at a speed of 50.0 m/s and at an elevation of 160 m drops a package. Two seconds later it drops a second package. How far apart will the two packages land on the ground?

Answer 38

100 m

Question 39

A 400-m tall tower casts a 600-m long shadow over a level ground. At what angle is the sun elevated above the horizon?

Answer 39

34°

Question 40

A jumper competing in the long-jump goes into the jump with a speed of 12 m/s at an angle of 20° above the horizontal. What is the horizontal range of the jump?

Answer 40

9.4 m