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A stone is dropped from top of a tower and travels 24.5 meter in last second of it`s journey. The height of the tower is ??

A stone is dropped from top of a tower and travels 24.5 meter in last second of it`s journey. The height of the tower is ??

Grade:9

1 Answers

Soumya Ranjan Mohanty
117 Points
6 years ago
let total time taken for the journey= n seconds.
given, u=0 and acceleration=a=g=9.8 ms^-2
formula for distance travelled in nth second=u+a/2(2n-1)
so here distance travelled in nth(last) second=24.5m=0+9.8/2(2n-1) =>24.5/4.9=2n-1=>5=2n-1=>2n=6=>n=3 seconds
So total time=3 seconds.
 
we know distance=u+1/2 * a * t^2
here let distance=height of tower=h, a=9.8 ms^-2,t=n=3 seconds
so h=0+1/2*9.8*3^2=4.9*9=44.1 metres.
 
therefore, height of tower is 44.1 metres.
 
thanks,
Soumya Ranjan Mohanty.

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