# A rubber ball is bounced from a height of 4 metres and bounces continuously. Each successive bounce reaches a height that is half the previous height. If the pattern of the maximum height reached...

A rubber ball is bounced from a height of 4 metres and bounces continuously. Each successive bounce reaches a height that is half the previous height. If the pattern of the maximum height reached during each bounce continues,

Determine an algebraic expression for the maximum height reached in the nth bounce.

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It is given that rubber ball bounce, half of the previous height. initially it bounces from 4m and starts to bounce.

Height of second bounce `= 4/2 =2m=4*1/2`

Height of third bounce `=2/2 =1 = 4*(1/2)^2`

Height of fourth bounce `=1/2 =4*(1/2)^3`

The motion of a bouncing of the follows a geometric series with a=4 and r=1/2

`T_2=4*(1/2)`

`T_3=4*(1/2)^2`

*So Maximum height reach in the nth bounce would be;*

`T_n = 4*(1/2)^(n-1)`

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