A ball bounces 1/2 its height each bounce. It is dropped from a height of one foot.
a) How many times does it bounce?
b) How far does it bounce?
c)How long does it bounce? Does it ever come to rest?
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Because, after every collision with the ground the ball will go up half of the height from which it was fallen. So, this process will continue for infinite number of bounces (h/2, h/4, h/8, h/16, h/32......)
distance travelled before first collision = h
distance travelled before second collision = 2*(h/2)
(rise h/2 and fall back)
distance travelled before third collision = 2*(h/4)
distance travelled before fourth collision = ...
The solution discusses how many times, how far and how long the ball bounces.