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A body took 't' sec. to come down from t...

A body took 't' sec. to come down from top of tower.Find the time taken to cover half the height of the tower .

Text Solution

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Let AB be the tower of height .h. m and the body taken .t. seconds to come down from A to B as shown in the figure .
Let C be the midpoint and hence `AC=h/2m`

Applying the above formula for both the cases, we get
`h=1/2"gt"^(2)` ...(1)` , h/2=1/2"gt"^(2)` ...(2)
Eliminating the unconcerned terms by dividing equation (1)by (2), we get
`(1)/(2)=h/(h//2)=(1/2"gt"^(2))/(1/2"gt"^(2))rArr 2=(t/t.)^(2) rArr t^(1^(2))=t^(2)/2rArrt^(1)=t/sqrt2s`
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