# Vector diagram problems: ```Physics
2010-2011
VHHS
Physics 1st Semester Final Review practice problems
For each of the following problems, ignore the effects of wind resistance unless
otherwise stated. Acceleration due to gravity is 9.8 m/s2.
Vector diagram problems:
1. Steve walks west 15 km and then south for 23 km. Draw a vector diagram showing the
magnitude and direction of his displacement.
2. While flying east at 130 km/hr, an airplane is blown north by the wind at 45 km/hr.
Find the resultant velocity of the plane? (remember, velocity involves both _____ &amp;
______ ) Include a vector diagram.
Motion Problems:
3. A rock is dropped from a cliff that is 50 m tall,
a. how long would it take to hit the ground?
b. How fast would that rock hit the ground?
c. What acceleration would the rock experience?
4.
Maria throws an apple vertically upwards from a height of 1.3 m above the ground
with an initial velocity of +2.4m/s.
a. Will the apple reach Maria’s friend in a tree house 5.3 meters above the ground?
b. If the apple is not caught, how long will it be in the air before it hits the ground?
Projectile problems:
5. A 2000 kg car traveling 25 m/s drives off a 120 m cliff.
a How many seconds after the car leaves the cliff does it crash to the ground below?
b. How far from the base of the cliff does the car land?
6. The water in a river is moving at a speed of 5 m/s before it approaches a 15 m vertical
drop (Waterfall).
a. How many seconds will it take a drop of water to reach the river below?
b. How many meters away from the base of the ledge will the water land?
7. A football is kicked with a velocity of 15 m/s at an angle of 30 degrees from the
horizontal.
a) What are the horizontal and vertical components of the initial velocity? Include a
diagram.
b) How long will the ball remain in the air?
c) What is the maximum height the ball will reach?
d) How far away from the tee will the ball land?
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Physics
2010-2011
VHHS
8. A golf ball is hit on a flat fairway with an initial velocity of 35 m/s at an angle of 55
degrees with the ground.
a) What are the horizontal and vertical components of the initial velocity? Include a
diagram.
b) How long will the ball remain in the air?
c) What is the maximum height the ball will reach?
d) How far away from the tee will the ball land?
Force diagram problems:
9. Steve pulls on Amy's arm to the left with 40 N of force while Henry pulls on her leg to
the left with 90 N of force. Assume that Amy has a mass of 65 kg and the floor is
frictionless.
a. Draw a force diagram showing all the forces acting on Amy. Include the magnitude of
b. What is the net force acting on Amy?
c. What is Amy's acceleration?
10. Tom yanks horizontally on the cord of her 3.75 kg iron with a 90 N force to drag it
across the bathroom floor. The frictional force acting on the iron is 15 N.
a. Draw a force diagram showing all forces (include force magnitudes) acting on the
iron.
b. What is the net force?
c. What will the acceleration of the iron be?
1
11. For the two body force problem to the right, calculate the
acceleration of M1
if M1 = 5.3 kg
M2 = 7.8 kg
2
Conservation of Energy Problems:
12. A 40 kg skate boarder starts from rest at the top of a 15 m hill.
a. What is his PE. KE and total energy at the top of the hill?
b. What is his PE, KE and total energy at the bottom of the hill?
c. What is his speed at the bottom of the hill?
d. At the top of a second hill, the skate boarder has a speed of 3 m/s. How high is the
second hill?
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Physics
VHHS
2010-2011
13. A 2000 kg car traveling 15 m/s runs out of gas at the top of a 4 m hill. The driver
allows the car to coast down the icy hill and up the subsequent icy hill without braking.
(Of course, this entire event is taking place in a vacuum!)
a. What is the PE. KE and total energy of the car at the top of the hill?
b. What is the PE, KE and total energy of the car at the bottom of the hill?
c. If an officer of the law is at the bottom of the hill checking the speed with radar,
will the driver be exceeding the 20 m/s speed limit? What was his speed? .
d. If the driver of the car lives at the top of the second hill, which is 10 m high, will
the car be able to coast to his driveway? If so, how fast will he be going? If not, how
high will the car travel before it comes to a stop?
14. A 2000 kg car traveling at 40 m/s suddenly slams on its brakes which supply a 1000 N
braking force. How far will the car skid before coming to a complete stop?
Conservation of Momentum Problems:
15. A 100 kg fullback running 5 m/s east is tackled by a 72 kg defensive back traveling
west at 6 m/s. They become entangled.
What is their velocity after the collision?
Who suffered the most from the collision and why?
16. A 150 kg bumper car traveling west at 4 m/s hits and bounces off a 200 kg bumper car
traveling west at 2 m/s. After the collision, the 150 kg car is traveling east at 1.5 m/s.
What is the momentum of the 200 kg car after the collision?
17. A 5 kg bowling ball traveling south at 5 m/s runs into a resting 0.15 kg bowling pin.
After the collision, the bowling ball travels south at 4.8 m/s. What is the velocity of
the bowling pin after the collision? Assume this is an elastic collision.
18. A 0.125 kg hockey puck moving at 25 m/s strikes a 0.350 kg ham which has been
dropped on the ice and is resting peacefully. The puck and ham slide off together to
pork paradise (Dubuque). What is their speed?
Circular Motion Problems:
19. A child moves with a speed of 4.3 m/s when 18.2 m from the center of a merry-goround.
a. What is the centripetal acceleration of the child?
b. If the child has a mass of 30.0 kg, what force acts on the child?
20. What is the maximum speed with which a 1900 kg car can round a turn of radius 80 m
on flat road if the coefficient of friction of 0.30? (DRAW FBD)
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Physics
2010-2011
VHHS
21. A 2 kg ball on a string is rotated about a circle of radius 10 m. The maximum tension
allowed in the string is 50 N. What is the maximum speed of the ball?
22. Two object are sitting next to each other on a desk. One has a mass of 115 kg the
other has a mass of 25 kg What is the attractive force between the two objects if
they are 30 cm away from each other? Do both objects feel the same attractive
force?
Torque Problems:
23. A uniform horizontal rod 4.0 m long is pivoted at the right end. If the bar weighs 4.5
N, what is the magnitude of torque produced by the bar?
24. A construction worker is trying to lift a bar of length 2.0m that has a mass of 15 kg.
If two buckets of tools, one of which has a mass of 10 kg and the other has a mass of
5 kg, located at each end of the bar, where does the construction worker have to pick
up the bar in order to balance everything out? Use the side with the more massive
bucket as the pivot point.
25. A 1.4 m seesaw is has two children on it. A 120 N child sits 40 cm from on end. Where
should a 60 N child sit so that the seesaw will again be balanced?
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Physics
2010-2011
V=∆x/t
VHHS
a=∆V/t
1 2
at
2
1
y  viy t  gt 2
2
v fx  vix  at
x  vix t 
v fy  viy  gt
vi2
sin 2
g


p  mv
R
Fnet  ma


F  t  p
v 2fx  vix2  2ax
v 2fy  viy2  2 gy
f  N
Fg  mg
KE 
1
(vix  v fx )t
2
1
y  (v fy  viy )t
2
x
1 2
mv
2
Elastic Collision Equation  m1v1i  m2 v2i  m1v1 f  m2 v2 f
Inelastic Collision Equation  m1v1i  m2 v2i  (m1  m2 )v f
ac 
v2
r
Fc 
mv 2
r
Fg 
Gm1m2
r2
G  6.67 x10 11
Nm 2
kg 2
  Fd
W  F  d cos 
W  KE
1 2
1
mvi  mghi  mv 2f  mgh f
2
2
PE g  mgh
P
PE s 
W
 Fv
t
1 mile  1609 meters
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1 2
kx
2
```