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A boy is standing on top of a tower of height $85 \,m$ and throws a ball in the vertically upward direction with a certain speed. If $5.25$ s later he hears the ball hitting the ground, then the speed with which the boy threw the ball is .......... $m / s$ (take, $g=10 \,m / s ^2$ and speed of sound in air $=340 \,m / s$ )
$6$
$8$
$10$
$12$
Solution

(b)
Given, sound of ball (hitting the ground) is heard $5.25$ s after the ball is thrown.
Sound of ball reaches top of tower in time,
$t_1=\frac{D}{s}=\frac{85}{340}=0.25 \,s$
So, ball reaches ground in time,
$t_2=5.25-0.25=5 \,s$
If $u=$ initial speed of ball at $t=0$, then for the ball,
$s=-85 m , a=-g=-10 \,ms ^{-2}, t=5 \,s$
Using, $\quad s=u t+\frac{1}{2} a t^2$
$-85=u({5})+\frac{1}{2}(-10)(5)^2$
$\Rightarrow \quad 5 u=125-85 \Rightarrow u=8 \,ms ^{-1}$