A stone is dropped from the peak of a hill. It covers a distance of 30m in last second of its motion. What is height of the peak?

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Answer 1 · 2017-04-15T12:51:53

$"peak height : "62.16" "meters$

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$"let the arrival time of Object from A to B be t. "$

$AC=1/2 g t^2$

$AB=1/2 g (t-1)^2$

$AC-AB=30" "meters$

$30=1/2 g t^2-1/2 g(t-1)^2$

$30=1/2g[t^2-(t-1)^2]$

$(30*2)/g=t^2-(t^2-2t+1)$

$60/g=cancel(t^2)-cancel(t^2)+2t-1$

$60/g+1=2t$

$(60+g)/g=2t$

$2t=7.12$

$t=(7.12)/2$

$t=3.56 sec$

$"peak height="AC=1/2*g*t^2$

$AC=1/2*9.81*(3.56)^2$

$AC=62.16" "meters$