From the top of a tower, a stone is thrown up and it reaches the ground in time ` t_1 `A second stone is thrown down with the same speed and it reaches the ground in time `t_2` A third stone is released from rest and it reaches the ground in time The correct relation between ` t_1,t_2` and `t_3` is :

Explanation

Let h= height of tower, u=speed of projection of stone 
`:.h=-ut_(1)+1/2"gt"_(1)^(2)=ut_(2)+1/2"gt"_(2)^(2)`
But h is also `=0 + 1/2 "gt"_(3)^(2)" or "ut_(2) +ut_(1)=1/2"gt"_(1)^(2)-1/2"gt"_2^2`
or `u(t_(2)+t_(1))=1/2g(t_(1)+t_(2))(t_(1)-t_(2))" or "u=1/2g(t_(1)-t_(2))`
`:. -1/2g(t_(1)-t_(2))t_(1)+1/2"gt"_(1)^(2)=1/2"gt"_(3)^(2)`
or `-t_(1)^(2) +t_(1)t_(2) +t_(1)^(2) = t_(3)^(2) " or " t_(1)t_(2) = t_(3)^2`