Question

If the energy of a ball falling from a height of 10 metres is reduced by 40%, how high will it rebound?

Answer 1

Given:

Height (h₁) = 10 m

PE₂ = PE₁ - PE₁ of 40%

Find: Height (h₂)

Formula: P.E. = mgh

Calculations:

PE₁ = mgh₁   ...(i)

PE₂ =  mgh₂  ...(ii)

PE₂ = PE₁ of 60%

Dividing equation (ii) by (i).

`"PE"_2/"PE"_1 = ("mgh"_2)/("mgh"_1)`

`(60%"PE"_1)/("PE"_1) = "h"_2/10`

`60/100 = "h"_2/10`

`"h"_2 = (60 xx 10)/100`

h₂ = 6 m

∴ The ball will bounce up to a height of 6 m when it hits the ground.