Scenario 1:
A ski jump in a local terrain park is built
with the dimensions in the diagram
below. During a competition, a skier
starts from rest, accelerates down the hill,
and performs a spectacular stunt in the
air, landing safely on the sloped landing
at the far side of the deck.
In the questions below, neglect air
resistance and friction, and use the
following values:
!=5m
ℎ=2m
! = 10 m
! = 20°
A
B
11. [MC3 – select only 1 answer] The skier is launched into the air at point A at an angle ! relative to the
horizontal. The skier lands at point B, and the landing ramp makes an angle ! relative to the horizontal, as
shown. To ensure a smooth landing, ! should match the skier’s direction of motion at point B. Given this,
which of the following is correct?
a. ! should be larger than ! (! > !)
b. ! should be smaller than ! (! < !)
c. ! should be equal to ! (! = !)
12. [MC5 – select up to 2 answers] The skier starts from rest at a height ! = 5 m above the top of the jump.
What is the horizontal component of the skier’s velocity when she launches off the jump at point A?
a. 9.3 m/s
b. 7.9 m/s
c. 6.2 m/s
d. 4.8 m/s
e. 3.4 m/s
13. [MC5 – select up to 2 answers] What is the skier’s speed when she lands at the very end of the deck (point
marked B)?
a. 39.2 m/s
b. 16.6 m/s
c. 11.7 m/s
d. 9.9 m/s
e. 6.3 m/s
Scenario 2:
A javelin is a narrow cylindrical spear thrown by athletes in the
Olympic Games. To throw a javelin, an athlete grips the spear with
her hand and exerts an effective normal force ! on the shaft. As
she throws the spear, her hand follows an approximately linear path
from A to B. She releases the javelin at point B when her arm is
completely extended above her shoulder (black dashed line
represents shoulder height).
B
A
✓
In the questions below, neglect air resistance and use the following values:
length of athlete’s arm: 60 cm; distance from A to B: 1.5 m; !!"#!"#$ = 600 g
14. [MC5 – select up to 2 answers] What is the work done by gravity on the javelin when it moves from point
A to point B?
a. 3.5 Joules
b. -3.5 Joules
c. 8.8 Joules
d. -8.8 Joules
e. 5.3 Joules
15. [MC5 – select up to 2 answers] The javelin’s speed at point A is 5 m/s. When the athlete releases the
javelin at point B, its speed is 26 m/s. What is the work done by the athlete’s hand on the javelin from point
A to point B? (Answers are rounded to nearest 50 Joules.)
a. 100 Joules
b. −150 Joules
c. 150 Joules
d. −200 Joules
e. 200 Joules
16. [MC3 – select only 1 answer] The athlete throws the javelin again, but this time the angle of her throw is
! = 45°. For this throw, the speeds of the javelin at points A/B (beginning/end of throwing motion) are the
same as before (A: 5 m/s; B: 26 m/s) and the distance between A and B is still 1.5 m. Compared to her first
throw, what is the work done on the javelin by friction from her hand?
a. Friction does no work in either throw.
b. The work done by friction is larger in her second throw (! = 45°) than it was in her first throw.
c. The work done by friction is smaller in her second throw (! = 45°) than it was in her first throw.
Scenario 3:
An amusement park ride starts by accelerating a car along a horizontal section of track using a large spring. To
help control the car’s speed, there is a rough patch of length ! between points A and B. After the rough patch,
the track bends up a hill. Other than the rough patch, friction and drag can be neglected.
Use the following values in the questions below:
!!"#$%& = 3.92 kN/m
!!"# = 400 kg (includes riders)
!=2 m
!! = 0.25 (for rough patch)
17. [MC5 – select up to 2 answers]The designers of the ride want the car to pass over the rough patch at least
four (4) times before coming to rest. What is the minimum distance the spring must be compressed initially
to ensure this happens?
a. 0.5 m
b. 1 m
c. 1.5 m
d. 2 m
e. 2.5 m
18. [MC5 – select up to 2 answers] The car is launched by the spring, and its speed at point A is measured to
be 20 m/s. How high up the hill will the car travel?
a. 23 m
b. 20 m
c. 18 m
d. 13 m
e. 10 m
19. [MC3 – select only 1 answer] The speed of the car at point B:
a. is always less than the speed at point A.
b. can be larger than the speed at point A.
c. can be equal to the speed at point A.
Scenario 4:
A man and a heavy cylinder are initially at rest at the right end of a
stationary boat, which sits in calm water. The man pushes the
cylinder to the left and it rolls to the other side of the boat, where it
is stopped by a wall attached to the left end of the boat. The boat
experiences no friction (drag) when moving through the water.
Use the following values in the questions below:
!=9m
!!"#$ = 170 kg
!!"# = 70 kg
!!"#$%&'( = 80 kg
20. [MC3 – select only 1 answer] When the cylinder moves from the right side of the boat to the left, in which
direction does the center of mass of the man + boat + cylinder system move?
a. To the left
b. To the right
c. The center of mass does not move
21. [MC5 – select up to 2 answers] It takes the cylinder !" = 3 s to travel from the left to the right end of the
boat. What is the average speed of the boat through the water while the cylinder is in motion?
a. 1.6 m/s
b. 1.4 m/s
c. 1.0 m/s
d. 0.75 m/s
e. 0 m/s
22. [MC5 – select up to 2 answers] The man walks to the left side of the boat to retrieve the cylinder. When
both the man and cylinder are at the left end of the boat, how far has the boat moved through the water
relative to the initial situation (both at right side of boat)?
a. 6.61 m to the right
b. 4.22 m to the right
c. 2.39 m to the right
d. 0 m: the boat doesn’t move
e. 2.39 m to the left
Scenario 5:
During a magic trick, a magician initially places three coins on a horizontal table in the positions shown.
23. [MC5 – select up to 2 answers] The magician slides the
nickel to a new location while the other two coins remain
in place. Where should the nickel be moved so that the
center-of-mass position for the system of coins is at the
origin, !!" , !!" = 0, 0 ?
y
!!"#$%&$ = 5.7 g
!!⃗!"#$%&$ = 〈0, 0〉 mm
x
quarter
a. !!"#$%& = −12.5, 37.5 mm
b. !!"#$%& = −12.5, 75 mm
c. !!"#$%& = −50, 150 mm
d. !!"#$%& = 0, 0 mm
nickel
!!"#$%& = 5.0 g
!!⃗!"#$%& = 〈−75, −50〉 mm
penny
!!"##$ = 2.5 g
!!⃗!"##$ = 〈25, −75〉 mm
e. !!"#$%& = −25, 37.5 mm
24. [MC5 – select up to 2 answers] The coins are replaced in the positions shown in the figure. Then the
magician uses his finger to flick the quarter to the left with speed 1.16 m/s. What is the center-of-mass
velocity for the system of coins?
a. !!" = −1.16, 0 m/s
b. !!" = 0, −1.16 m/s
c. !!" = −0.09, 0 m/s
d. !!" = −0.43, 0 m/s
e. !!" = −0.50, 0 m/s
25. The coins are replaced in the positions shown in the figure. Then the positions of the penny and quarter are
exchanged. After the exchange, in which direction does the position of the center-of-mass move relative to
the configuration shown in the figure?
a. Down and to the left.
b. Down and to the right.
c. Up and to the left.