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?
Answers
Reiny
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.
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.