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Homework Problems
1. (a) A ball is thrown straight up with velocity v. Find an equation for
the height to which it rises.
(b) Generalize your equation for a ball thrown at an angle
.
above hori-
zontal, in which case its initial velocity components are v
x
=v cos
.
and v
y
=v
sin
.
.
2. At the Salinas Lettuce Festival Parade, Miss Lettuce of 1996 drops her
bouquet while riding on a float. Compare the shape of its trajectory as
seen by her to the shape seen by one of her admirers standing on the
sidewalk.
3 . Two daredevils, Wendy and Bill, go over Niagara Falls. Wendy sits in
an inner tube, and lets the 30 km/hr velocity of the river throw her out
horizontally over the falls. Bill paddles a kayak, adding an extra 10 km/hr
to his velocity. They go over the edge of the falls at the same moment, side
by side. Ignore air friction. Explain your reasoning.
(a) Who hits the bottom first.
(b) What is the horizontal component of Wendy's velocity on impact.
(c) What is the horizontal component of Bill's velocity on impact.
(d) Who is going faster on impact.
4. A baseball pitcher throws a pitch clocked at v
x
=73.3 mi/h. He throws
horizontally. By what amount, d, does the ball drop by the time it reaches
home plate, L=60.0 ft away. (a) First find a symbolic answer in terms of L,
v
x
, and g. (b) Plug in and find a numerical answer. Express your answer in
units of ft. [Note: 1 ft=12 in, 1 mi=5280 ft, and 1 in=2.54 cm]
L=60.0 ft
d=.
v
x
=73.3 mi/hr
5 S. A cannon standing on a flat field fires a cannonball with a muzzle
velocity v, at an angle
.
above horizontal. The cannonball thus initially has
velocity components v
x
=v cos
.
and v
y
=v sin
.
.
(a) Show that the cannon’s range (horizontal distance to where the can-
nonball falls) is given by the equation R =
2v
2
sin
.
cos
.
g
.
(b) Interpret your equation in the cases of
.
=0 and
.
=90
°
.
SA solution is given in the back of the book.A difficult problem.
A computerized answer check is available.
.
A problem that requires calculus.
Homework Problems