2834 WordsOct 15, 201312 Pages

Assignment 1: Kinematics in 2 and 3 Dimensions
Due: 2:00am on Saturday, September 4, 2010
Note: To understand how points are awarded, read your instructor's Grading Policy.
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Arrow Hits Apple
An arrow is shot at an angle of
above the horizontal. The arrow hits a tree a horizontal distance
away, at the same height above the ground as it was shot. Use
for the
magnitude of the acceleration due to gravity.
Part A
Find
, the time that the arrow spends in the air.
Hint A.1
Find the initial upward component of velocity in terms of D.
Hint not displayed
Hint A.2
Find the time of flight in terms of the initial vertical component of velocity.
Hint not displayed
Hint A.3*…show more content…*

Correct
A Wild Ride
A car in a roller coaster moves along a track that consists of a sequence of ups and downs. Let the x axis be parallel to the ground and the positive y axis point upward. In the time interval from to s, the trajectory of the car along a certain section of the track is given by
,
where
is a positive dimensionless constant.
Part A
At
Hint A.1
is the roller coaster car ascending or descending?
How to approach the problem
Hint not displayed
Hint A.2
Find the vertical component of the velocity of the car
Hint not displayed
ANSWER:
ascending descending Correct
Part B
Derive a general expression for the speed
Hint B.1
of the car.
How to approach the problem
Hint not displayed
Hint B.2
Magnitude of a vector
Hint not displayed
Hint B.3
Find the components of the velocity of the car
Hint B.3
Find the components of the velocity of the car
Hint not displayed
Express your answer in meters per second in terms of
and .
ANSWER:
=
Correct
Part C
The roller coaster is designed according to safety regulations that prohibit the speed of the car from exceeding . Find the maximum value of allowed by these regulations.
Hint C.1
How to approach the problem
To comply with the regulations, the speed of the car cannot exceed the given safety limit at any time. Thus, you need to determine what the

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