# 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

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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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(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))`