Unit 2 Test: 2-D motion
Physics
Name: ___________________
March 8, 2012
v = vo + at
x = ½( v + vo ) t
A2 + B2 = R2
x = xo + vot + ½ at2
v2 = vo2 + 2a (x - xo)
SOH,CAH,TOA
vy = voy + gt
y = ½( vy + voy ) t
gravity = -10.0m/s2
y = yo + voyt + ½ gt2
vy2 = voy2 + 2g (y - yo)
vox = v cos 
x = vx t
voy = v sin 
Multiple Choice Answers (____ / 36 points) 2 pts each
Record your answers for the multiple choice questions at the back of this packet below:
1) ____
2) ____
3) _____
7) ____
8) ____
9) _____
4) _____
5) _____
6) _____
1) A spider is placed at the origin (0,0) of a piece of graph paper. It crawls 9.0 cm at
an angle of 0o, 5.0 cm at an angle of 90o, and finally 7.0 cm at an angle of 200o.
a. (4 pts) Draw a reasonable sketch of these movements on a piece of graph
paper.
b. (2 pts) What distance did the spider travel?
c. (3 pts) What is the final displacement of the spider after the three
movements?
2) An arrow is shot from a height of 7.6 meters with an initial speed of 97.5 m/s at
horizontally and then strikes and sticks in a tree in its path. The tree is 90.0 m from
the launch site. Neglect any aerodynamic effects and air resistance in answering the
questions that follow.
Not drawn to scale
0o

7.6 m
90.0 m
a. (3 pts) Identify the firing velocity of the arrow initial x and y components.
vox =
voy=
b. (1 pt) Does the vox change during flight?
c. (1 pt) Does the voy change during flight?
d. (3 pts) How long is the arrow in flight (in seconds) if the tree is 90.0 m
away from the cliff?
e. (3 pts) How high above the ground will the arrow stick in the tree?
Answer one (1) of these two (2) questions (3 pts)
f. What is the speed of the arrow just before it strikes the tree?
g. What angle relative to the horizontal as shown in the diagram (), will the
arrow form when it sticks in the tree?
Think and Explains
3) You are kicking a soccer ball against the kick board out behind the cafeteria. You
are working at hitting the same spot on the kick board over and over again from
different distances. You are able to kick the ball with the same pace (or initial
velocity) and the same angle (20o) each time.
Read about all four kicks, then do the drawings…
a. Your 1st kick is from 40 meters away. It lands just short of the kick board.
You notice that during its flight the soccer ball never went any higher than
the kick board, 4.1 meters. Draw its path from your foot to the board.
Label it A and make the line dark.
b. Your 2nd kick is from 25 meters away. It strikes the kick board 2.4 meters
up, exactly where you want it, just under the cross bar. Draw its path from
your foot to the board. Label it B and make the line dashed.
c. Your 3rd kick is from 35 meters away. It strikes the kick board 2.4 meters
up, exactly where you want it, again, just under the crossbar. Draw its
path from your foot to the board. Label it C and make the line with dots.
d. Your 4th kick is from 30 meters away. It strikes the top of the kick board
4.1 meters up, over the crossbar. Draw its path from your foot to the
board. Label it D and make the line thin.
40m
35m
30m
25m
20m
15m
10m
5m
4m
3m
2m
1m
0m
0m
e. How is it possible to have the same initial velocity and angle reach the
same height with two different ranges? Be detailed here…
f. If you had to kick a fifth time from 30 meters what could you do
differently to hit the board 2.0 meters up? Be specific.
4) A ball is launched at an angle of 35o from the ground with an initial velocity of 15
m/s on a planet with no atmosphere and a gravity of -10m/s2.
a. What is the magnitude and direction of the ball’s vertical acceleration …
i. …while it is moving upward?
ii. …when it is at its greatest height?
iii. …when it is moving downward?
b. What is the magnitude of the ball’s horizontal acceleration…
i. …while it is moving upward?
ii. …when it is at its greatest height?
iii. …when it is moving downward?
c. What is the ball’s vertical velocity…
i. …when it is at its highest point?
ii. …an instant before it hits the ground?
d. Complete a ROUGH Sketch the ball’s graph for…
(don’t worry about scale or values, just the shapes of these six graphs)
Vertical
displacement vs. time
Vertical
velocity vs. time
0 m/s
Horizontal
displacement vs. time
0 m/s2
Horizontal
velocity vs. time
0 m/s
Vertical
acceleration vs. time
Horizontal
acceleration vs. time
0 m/s2
5) Do two (2) of these three (3) shorter Think and Explains…
10 m/s
5 m/s
6a. The cart shown above is moving to the right at a constant velocity of 5
m/s when it launches a sphere vertically upward at 10 m/s. If the cart
maintains a constant horizontal velocity, the sphere will most likely land…
a. in front of the cart
b. on the cart
c. to the left of the cart
d. behind the cart
e. to the right of the cart
because...
6b. A friend who is competing in the long jump asks you to explain the physics of this
event. What advice do you give your friend about the jumping angle? Why?
Include a diagram of your friend’s take off with as much information as you can
think of…
6c. A zoologist, standing on a cliff on an island free of air resistance, aims a tranquilizer gun at
a monkey hanging from a distant tree branch. The barrel of the gun is horizontal. Just as the
zoologist pulls the trigger, the monkey lets go of the branch and begins to fall. Will the dart hit
the monkey? Why or why not?
Multiple choice Questions
1. To throw a ball as far as possible, you should throw it at which angle:
a. 30 o
b.) 60o
c.) 45 o
d.) 90 o
e. the angle doesn’t matter – it only depends on the velocity
2. To launch a projectile as high as possible, you should launch it at which
angle:
a. 30 o
b.) 60o
c.) 45 o
d.) 90 o
e. the angle doesn’t matter – it only depends on the velocity
3. Which pair of angles would have the same range if a projectile were fired
with the same initial velocity?
a. 80 o and 120o
b. 40 o and 50 o degrees
c. 15 o and 15 o degrees
d. 85 o and 95 o degrees
e. the angle doesn’t matter – it only depends on the velocity
Base your answers to Questions 4, 5 and 6 on the information below
A river has a current of 6.0 m/s East.
A boat with a constant velocity of 8.0 m/s in still water is attempting to cross
the river.
NOT DRAWN TO SCALE
Current = 6.0 m/s East
boat = 8.0m/s North
4. If the boat heads due North while crossing the river, what will its overall
speed be?
a. 5.3 m/s
b.) 6.9 m/s c.) 7.0 m/s d.) 14 m/s
e.) 10. m/s
5. If the boat heads due North while crossing the river, what angle will it travel?
a. Due North
b.)37
c.) 41
d.) 49
e.) 53
6. What is the fastest speed the boat could attain traveling in any direction in
the river?
a. 2 m/s
b.) 14 m/s
c.) 10 m/s
d.) 7 m/s
N
VP
E
VW
7. The diagram above shows the velocity with which the wind (VW) is blowing on an
plane that is flying with a velocity (VP). Both vectors are drawn to scale. The
approximate direction the airplane is going to move is…
a. North
b. South
c. East
d. West
8. True or False: perpendicular vectors act independently
9. Which of the following diagrams best represents the acceleration of any
projectile launched in any direction on Earth?