A body is thrown vertically upwards from `A`. The top of a tower . It reaches the ground in time `t_(1)`. It it is thrown vertically downwards from `A` with the same speed it reaches the ground in time `t_(2)`, If it is allowed to fall freely from `A`. then the time it takes to reach the ground.
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Explanation

(A): `-h=ut_(1)-1/2g t_(1)^(2) …(i)`
(B) `h=ut_(2)+1/2g t_(2)^(2) …(ii)`
From (i), `u=-h/t_(1)+1/2g t_(1)`
From (ii), `u=h/t_(2)-1/2 g t_(2)`
`-h/t_(1)+1/2 g t_(1)=h/t_(2)-1/2 g t_(2)`
`(h(t_(1)+t_(2)))/(t_(1)t_(2))=1/2g (t_(1)+t_(2))`
`h=1/2g t_(1)t_(2)`
(c ): `h=1/2 g t^(2)`
`1/2g t_(1)t_(2)=1/2g t_(2)`
`t=sqrt(T_(1)t_(2))`