Expert: Sherman D. - 11/7/2005

Question
had galileo dropped a cannonball from the Tower of Pisa, 179 ft. above the ground, the ball's height above ground t sec into the fall would have been s=179-16t^2.

1) what would have been the ball's velocity, speed, and acceleration at time t?
2) about how long would it have taken the ball to hit the ground?
3) what would have been the ball's velocity at the moment of impact?

Answer
1.)
s = 179 - 16t^2
s = -16t^2
s = -32t^(2 - 1)
s = -32t

Velocity = -32t

s = 179 - 16t^2, which was given

v = -32t
v = -32t^(1 - 1)
v = -32

Acceleration = -32

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2.)
s = 179 - 16t^2
0 = -16t^2 + 179
16t^2 = 179
t^2 = 179/16
t = (sqrt(179))/4
t = 3.345
or
ANS : t = about 3.345 seconds

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3.)
v = -32t
v = -32(sqrt(179)/4)
v = -8sqrt(179)
v = -107.03
or
ANS : v = about -107 ft/s