Question

When a Superball bounces it is claimed that the height of any bounce is 90% of the height of the last bounce. If a Superball is dropped out of a second story window at the height of 200 feet. On which bounce would it bounce just one foot?

Answer 1

on 1st bounce goes up .9(200) ft
on 2nd bounce goes up .9(.9)(200) ft = .9^2 (200)
on 3rd bounce goes up .9^3 (200) ft

on nthe bounce goes up .9^n (200) ft
but that is supposed to be 1

.9^n (200) = 1
.9^n = 1/200 = .005
take log of both sides
n log .9 = log .005
n = log .005/log .9 = appr 50.3

check:
bounce #50 = 200(.9^50) = 1.03 ft
bounce #51 = 200(.9^51) = .93 ft

the 50th bounce is closes to 1 ft.