A stone is thrown upwards from the top of a tower with some initial speed and it reaches the ground in second. Now it is allowed to fall with the same initial speed downward and it reaches the ground in 1 second In how much time will it reach the ground if the stone is allowed to fall freely under gravity from the same place:

Options

A. `((t_1+t_2)/(2))`
B. `((t_1-t_2)/(2))`
C. `sqrt(t_1 t_2)`
D. `(t_1 +t_2)`

Answer

c

Explanation

The equation of motion in three cases are :
`h=-ut_(1)+(1)/(2)g t_(1)^(2)`
`h=ut_(2)+(1)/(2)g t_(2)^(2)`
`h=0+(1)/(2)g t^(2)`
Using `(1)/(2) g t^(2) =(1)/(2)g t_(1) t_(2) implies t=sqrt(t_1 t_2)`