Question

A table tennis ball is dropped from a height of 5ft. The ball rebounds to 60% of its previous height after each bounce.

Write an infinite geometric series to represent the distance that the ball travels after it initially hits the ground. (hint, the ball travels up and down on each bounce).

please help fast

Answer 1

After it initially hits the ground, the ball will travel
2(5)(.6) + 2(5)(.6)^2 + 2(5)(.6^3) + ....
= 10( .6 + .6^2 + .6^3 + .... )
or
= 6 + 6(.6) + 6(.6^2) + ...

a = 6, r = .6 , sum∞ = a/(1-r) = 6/.4 = 15