A rubber ball dropped on a hard surface takes a sequence of bounces, each one 2/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled after it hits the surface the fifth time? Be sure to account for both drop and rebound distances.

Question

A rubber ball dropped on a hard surface takes a sequence of bounces, each one 2/5 as high as the preceding one. If this ball is dropped  from a height of 10 feet, what is the total vertical distance it has traveled after it hits the surface the fifth time? Be sure to account for both drop and rebound distances.

anonymous · Answer

h(1) = 10  down  hit #1
h(2) = 0.4 h(1) = 4 up and 4 down  hit #2
h(3) = 0.4 h(2) = 1.6 up and 1.6 down   hit #3
h(4) = 0.4 h(3) = 0.64 up and 0.64 down    hit #4
h(5) = 0.5 h(4) = 0.256 up and 0.256 down and stop  hit #5

total = 10 + 8 + 3.2 + 1.28 + .512 = 22.99

but check my math to be safe.