Extra Credit Problems
A rock is dropped from rest into a well.
The sound of the splash is heard 3.25 seconds
after the rock is released from rest.
The speed of sound in air is 336 m/s.
How far below
the top of the well is the surface of the water?
(Chapter 2, #60)
H = 47.39 meters
Setting a new world record in a 100 meter race, Maggie and Judy cross the finish line
in a dead heat, both taking 10.2 seconds.
Accelerating uniformly, Maggie took 2 seconds
and Judy took 3 seconds to attain maximum speed, which they maintained for the rest of
a) What was the acceleration of each sprinter?
b) What were their respective
c) Which sprinter was ahead at the 6 second mark, and by how
(Chapter 2, #53)
a) 5.43 m/s
b) 10.9 m/s
The acceleration of a marble in a certain fluid is proportional to the speed of the
marble squared, and is given by a = -3.00v
for v > 0.
If the marble enters this fluid with
a speed of 1.50 m/s, how long will it take before the marble’s speed is reduced to half of
its initial value?
A pirate has buried his treasure on an island with five trees, located at the following
points: A (30 m, -20 m), B (60 m, 80 m), C (-10 m, -10 m), D (40 m, -30 m), and E
(-70 m, 60 m).
His ship’s log instructs you to start at tree A and move toward tree B, but
to cover only half the distance between A and B.
Then move toward tree C, covering one
third the distance between your current location and C.
Next, move toward D, covering
one fourth the distance between where you are and D.
Finally, move towards E, covering
one fifth the distance between you and E, stop, and dig.
What are the coordinates of the
point where his treasure is buried?
(Chapter 3, #59)
(10 m, 16 m)
A skier leaves the ramp of a ski jump with a velocity of 10.0 m/s, 15 degrees above
the horizontal (this is actually a Winter Olympics sport).
The slope of the mountain is
inclined at 50 degrees and air resistance is negligible.
a) the distance from the
ramp to where the jumper lands
b) the velocity components just before the landing.
(Chapter 4, #59)
= 9.66 m/s
= -25.5 m/s