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From the top of a tower, two balls are t...

From the top of a tower, two balls are thrown horizontally with velocities `u_(1)` and `u_(2)` in opposite directions. If their velocities are perpendicular to each other just before they strike the ground, find the height of tower.

Text Solution

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Time taken to reach ground `t=sqrt((2h)/(g))`
at the time of reaching ground respective velocities are
`overset(vec)v_(1)=u_(1)hati+"gt"hatj, overset(vec)v_(2)=-u_(2)hati+"gt"hatj`
Given `overset(vec)v_(1).overset(vec)v_(2)=0, t=(sqrt(u_(1)u_(2)))/(g)`
`:. sqrt((2h)/(g))=(sqrt(u_(1)u_(2)))/(g) rArr h=(u_(1)u_(2))/(2g)`
is the height of the tower.
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