Galileo Galilei
Exercises

An object in freefall is accelerated
16 ft/sec^{2} by gravity. If it takes exactly 4 seconds to
fall to the ground, at what height was it dropped? [Hint: Use the
mean speed law.]

Amy is driving along when she notices
her friend Bill's car in her rearview mirror. At the moment that
Bill speeds past her at 60 mph = 88 ft/sec, Amy starts accelerating at
a rate of 1 ft/sec per second from her initial speed of 50 mph = 73 ft/sec
to catch up with him. (a) Draw a graph of their speeds as functions of
time, with 0 seconds corresponding to the time at which Bill first passes
Amy; according to the mean speed law, how long will it take for Amy to
catch up with Bill? (b) How fast will Amy be going when she overtakes
Bill? (c) How far away from the point that Bill passed her will she
pass Bill? (d) When, in this period of time, is Amy furthest behind
Bill?

Suppose a rocket gains speed v
(measured in m/sec) according to the formula v = 20t^{2}
where t is the time after liftoff in seconds. How far will
the rocket travel in its first 10 seconds of flight? [Hint: write a suitable
integral to answer the question.]

A cannonball is fired straight out
from the top of the battlements of a castle onto the plain 100 ft beneath
at a speed of 60 ft/sec. Use the Galilean equations of motion for
the cannonball (and g = 32 ft/sec^{2}) to determine (a)
how long it takes for the ball to fall to the ground, and (b) what the
range of the shot is (that is, how far from the castle wall the ball strikes
the ground).

In the situation of the previous problem,
if the cannonball strikes the top of a seige tower exactly two seconds
after it is fired, how tall is the tower?
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last modified 11/7/02
Copyright(c) 2000. Daniel E. Otero