From the top of a tower, a stone is thrown up. It reaches the ground in $5$ $s$. A second stone is thrown down with the same speed and reaches the ground in $1$ $s$. A third stone is released from rest and reaches the ground in

The correct option is C $\sqrt{5}$ $s$
let height of tower is $H$, acceleration due to gravity is $a$,

case 1) initial velocity is $-u$ (assuming downward direction as positive.

then $H=-ut+\frac{1}{2}a{t}^2=>H=-5u+\frac{25}{2}a$

for case 2) initial velocity is $u$

then $H=ut+\frac{1}{2}a{t}^2=>H=u+\frac{1}{2}a$

multiplying 2nd with 5 and adding both equation we get

$6H=15a=>H=2.5a$

now for 3rd case $u=0$, we get $2.5a=\frac{1}{2}a{t}^2=>t=\sqrt{5}sec.$