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1. (40 points)
In a scene from Harry Potter’s latest
sequel, a master sorcerer holding a golden egg stands on a bridge above the
ground. On a concrete track
below, a young sorcery student rides on a motorized
scooter and moves to the right toward
the bridge with steady speed 14.00 m/s. See schematic
below. Dimensions not necessarily to scale.
At t = 0, the student is
an initial horizontal
distance D from the base of the bridge and begins to slow
down with constant acceleration of
magnitude 3.00
m/s2. At the same moment, the
master makes a quick calculation and throws the egg vertically up with speed 6.00 m/s such that
the student catches the egg as he
moves under the bridge. Assume the
master releases the egg when her hand is
48.00 m above the ground. Assume g = 9.8 m/s2. The
student catches the egg in a cushioned bucket held a distance 1.20 m above the ground.
SHOW ALL WORK . LABEL
ALL PARTS. Write the letter at the top of the work for
that part.
(a) (16 points) What is the
speed of the student when he catches the egg?
(b) (15 points) What is the speed of the egg just before
the student catches it?
(c) (3 points) What
is the average velocity of the student between t = 0 and the moment he
catches the egg? Assume rightward is
the positive direction of motion for the student.
(d) (3 points) What is the average
velocity of the egg between t = 0 and the moment the student catches it? Assume upward is the positive direction of
motion for the egg.
(e) (3 points) What is the initial
horizontal distance D?
2. (40 points) In a deleted scene from the movie “Unstoppable” , a runaway
freight train is 1.00x10 2
m in front of an unmanned maintenance train at t = 0. Assume rightward is the positive direction
of motion. See the schematic below of the two trains at t
= 0. Dimensions shown not necessarily to scale.
The freight train has initial velocity + 25.0 m/s and begins
to slow down with constant
acceleration of magnitude 1.00 m/s2.
The maintenance train has constant velocity + 10.0 m/s.
SHOW ALL WORK . LABEL
ALL PARTS. It may be helpful to sketch the position versus
time graphs of both trains on the same x vs t axes.
(a) (15 points) What is the velocity
of the freight train when the two trains collide? In what
direction is the freight train moving at the moment of collision, left
or right? Explain
(b) (4 points) What is the average velocity of the
freight train between t = 0 and the moment
of collision?
(c) (15 points) At what time is the
velocity of the freight train equal
to the velocity of the maintenance train?
(d) (6 points) Before they collide, what is the maximum distance between the freight
train and the maintenance train?
3. (40 points) Two forces  and  act at a point. The magnitude of is 8.00 N and its direction is 60.0 degrees above the x-axis in the second quadrant. The magnitude of is 5.00 N and its direction is 53.1 degrees below the x-axis in the third quadrant. This problems deals with vector addition
and the resultant force  . SHOW WORK, LABEL
PARTS.
(a) (9 points) What is the x-component of the resultant force?
(b) (9 points) What is the y-component of the resultant
force?
(c) (10
points) What is the magnitude of the
resultant force?
(d) (4 points) In what quadrant does the resultant force
point?
(e) (4 points) What angle does the resultant force make with the
x-axis?
(f) (4 points) On the axes below, make a sketch of the
resultant force with its tail at the
origin. Label the angle the resultant
force makes with the x-axis. Thank you.
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