ball is dropped from a height of 1.60 m and rebounds to a height of 1.20 m. Approximately how many rebounds will the ball make before losing 90% of its energy?

the ball rebounds 8 times before losing 90% of its energy

Explanation:

given information:

height, h₁ = 1.6 m

rebound height, h₂ = 1.2 m

energy loss = 90% = 0.9

first we can calculate the loss energy after the rebound

energy loss = 1 - [ (height of rebound/height of the ball) ^n

where

n = number of the bounce

energy loss = 1 - (h₂/h₁) ^n

0.9 = 1 - (1.2/1.6) ^n

(0.75) ^n = 1 - 0.9

n log 0.75 = log 0.1

n = log 0.1/log 0.75

= 8 bounces