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