From the top of a tower a stone is thrown up which reaches the ground in time `t_(1)`. A second stone thrown down with the same speed reaches the ground in a time `t_(2)`. A third stone released from rest from the same location reaches the ground in a time `t_(3)`. then:

Options

A. `(1)/(t_(3)) = (1)/(t_(1)) + (1)/(t_(2))`
B. `t_(3)^(2) = t_(1)^(2) - t_(2)^(2)`
C. `t_(3) = (t_(1) + t_(2))/(2)`
D. `t_(3) = sqrt(t_(1) t_(2))`

Answer

D

Explanation

`-H = ut_(1) - (1)/(2) g t_(1)^(2)`
`H = u t_(2) + (1)/(2) g t_(2)^(2)`
`H = (1)/(2) g t_(3)^(2)`