Practice Packet for Chapter 3: Two Dimensional Motion and Vectors
Name ______________________
Use your notes and chapter 3 in your book (pages 81-103) to answer the following questions.
Adding Vectors and Resolving Vectors
1) Compare linear motion to nonlinear motion.
Linear motion moves in one dimension and nonlinear motion moves in a curved path.
2) Define scalar quantity. Give three examples.
A scalar quantity has only magnitude. Examples are mass, volume, speed, time.
3) Define vector quantity. Give three examples.
A vector quantity has magnitude and direction. Examples are displacement, velocity, acceleration, and force.
4) If two vectors have unequal magnitudes can their sum equal zero? Explain.
No, the vectors must be equal in magnitude and opposite in direction.
5) What is a resultant vector?
A resultant vector is the sum of 2 or more vectors.
6) How are two vectors related when they sum to zero?
The vectors are equal in magnitude and opposite in direction.
7) If a car travels 30 km east and then 20 km west, what is the distance that it traveled?
The distance is 50 km.
8) If a car travels 30 km east and then 20 km west, what is the displacement of the car?
The displacement is 10 km east.
9) If an airplane that travels 200 km/hr heads directly against a 40 km/hr wind, what is the speed of the airplane
with respect to the ground?
The speed is 160 km/hr.
For the following problems you must show your work including a drawing with the x-component, y-component
and resultant vectors.
10) What is the velocity of a car traveling 120 km/hr east and then 200 km/hr south?

120 km/hr
V = 233.2 km/hr
 = 59.1o south of east
200 km/hr
11) You walk 2 km north, 6 km west, 3 km east, and then 8 km south. What is your displacement?
2 km
6 km
3 km
d = 6.7 km

3 km
 = 63.6o south of west
6 km
8 km
12) There is a 22.0 km wide river running north and south with a constant current of 12.0 km/hr south. A boat starts
out at a constant velocity of 25.0 km/hr east. What is the velocity of the boat?
25 km/hr
V = 27.7 km/hr
12 km/hr

 = 25.7o south of east
13) Find the x-component and y-component of an object moving at 34 m/s at an angle of 25o north of west.
34 m/s

 y = 14.4 m/s north
 x = 30.8 m/s west
Relative Motion Problems
14) You are in a car moving a constant velocity of 40 km/hr going east. Your best friend is in a car moving on the
same straight road at 72 km/hr going west. Draw a picture of the cars.
60 km apart
Me: 40 km/hr
Friend: - 72 km/hr
What is the relative velocity of your car to your friend’s car?
Vrel = 112 km/hr
If you start 60 km apart, how long will it take until you pass each other (or crash head on)?
 t = 0.54 hours
What is the displacement of your car when the cars meet?
 x = 21.6 km East
15) A car is traveling east at a constant velocity of 50 km/hr. Another car on the same straight, level road is traveling
east at a constant velocity of 65 km/hr. The slower car is 24 km in front of the faster car. Draw a picture of the
cars.
24 km apart
65 km/hr East
50 km/hr East
What is the relative velocity of the faster car to the slow car?
Vrel = 15 km/hr
How long will it take the faster car to catch up to the slower car?
 t = 1.6 hours
What is the displacement of both cars when the slower car catches the faster car?
Fast car:  x = 104 km East
Slow car:  x = 80 km East
Projectile Motion
16) Define projectile motion.
Projectile motion is the motion of objects that are thrown or launched into the air and are subject only to gravity.
17) In the absence of air resistance, why does the horizontal component of velocity for a projectile remain constant
while the vertical component changes?
There is no force acting in the horizontal direction so the horizontal component of the velocity doesn’t change. The force
of gravity acts in the vertical direction so the object accelerates.
18) How does the downward component of the motion of a projectile compare with the motion of free fall?
They are the same.
19) At the instant a ball is thrown horizontally over a level range, a ball held at the side of the first is released and
drops to the ground. If air resistance is neglected, which ball strikes the ground first? Explain your answer.
They hit the ground at the same time. Both balls are moving the same distance and both are accelerated due to gravity.
20) A projectile is launched vertically at 100 m/s. If air resistance can be neglected, at what speed will it return to at
its initial level?
The speed will be the same: 100 m/s
21) Suppose you drop an object from an airplane traveling at a constant velocity and air resistance doesn’t affect the
falling object. Draw its falling path as observed by someone at rest on the ground, not directly below but off to
one side.
What would be the falling path as observed by you looking downward from the airplane ignoring air resistance?
The path would be straight downward.
Where would the object strike the ground relative to you in the airplane ignoring air resistance?
The object would hit directly below the plane.
Where would it strike if air resistance affects the fall?
The object would hit the ground behind the plane.
22) A projectile is fired straight upward at 141 m/s. How fast is it moving upward at the instant it reaches the top of
its trajectory?
The speed is 0 m/s.
Suppose instead it were fired upward at a 45o angle. What would the y component of its velocity be the top of
its trajectory?
The y component of the velocity would be 0 m/s.
For all of these problems ignore the effects of air resistance. Draw a picture to help you visualize the problem. Show all
your work and the correct units for full credit.
23) A ball is projected horizontally off of the top of a cliff with a speed of 15 m/s. If the cliff is vertical and its height
is 56 m, how long does it take the ball to hit the ground?
Vx = 15 m/s
 x = -56 m
 t = 3.3 sec
24) In the above problem, what horizontal distance from the base of the cliff does the ball land?
 x = 49 .5 m
25) One crazy physics teacher was standing on top of tall building and wondered what the height of the building
was. The teacher threw a physics book (that was all she ever carried) horizontally off the building at 4.0 m/s. The
teacher found the book, open to chapter 3. The book was 16 meters from the base of the building. How long did
it take the book to fall?
Vx = 4.0 m/s
 t = 4 sec
 x = 16 m
26) What is the height of the tall building?
Height = 78.4 m
27) Have you ever watched movie where people fall into a pool below their balcony? How long would it take to
jump into the pool if it is 15 meters out from the bottom of their balcony that is 75 meters high?
 y = -75 m
 t = 3.9 sec
 x = 15 m
28) For the above problem, how fast would a person have to jump horizontally to reach the pool instead of the
pavement?
Vx = 3.8 m/s
29) How high is a cliff if it takes 6 seconds for a rock to hit the ground below after the rock is thrown horizontally off
the cliff?
Height = 176.4 m
30) Why doesn’t it matter how fast you throw the rock?
The downward motion of a horizontally thrown projectile is the same as the free fall of an object.