A particle is projected from the ground at an angle such that it just clears the top of a polar after `t_1` time its path. It takes further `t_2` time to reach the ground. What is the height of the pole ?

Explanation

Height of the pole is equal to vertical displacement at `t_(1)` instant.
Vertical displacement `y=v_(y)t_(1)+(1)/(2)a_(y)t_(1)^(2)-(1)/(2)"gt"_(1)^(2)`....(i)
and total flight time `t_(1)+t_(2)=(2u_(y))/(g)rArru_(y)=(g)/(2)(t_(1)+t_(2))`
ut value `u_(y)` in equation (i) `y=(g)/(2)(t_(1)+t_(2))t_(1)-(1)/(2)g(t_(1))^(2)=(1)/(2)"gt"_(1)t_(2)`. so height of the pole `=(1)/(2)"gt"_(1)t_(2)`