A body projected vertically upwords from the top of a tower reaches the ground in `t_(1)` second . If it projected vertically downwards from the some top with same velocity ,it reaches the ground in `t_(2)`seconds . If it is just dropped from the top it reaches the ground in t second .prove that `t=sqrt(t_(1)t_(2))`

Options

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

Answer

B

Explanation

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