Question

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 (take, $g \,= \,10\, m / s^2 $ and speed of sound in air $= 340\, m/s$)

• A. $6\, m/s$
• B. $8\, m/s$
• C. $10\, m/s$
• D. $12\,m/s$

Answer 1

Answer: (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, $s=ut +\frac{1}{2}at^{2}$
$-85=u \left(5\right)+\frac{1}{2}\left(-10\right)\left(5\right)^{2}$
$\Rightarrow 5u =125 -85\Rightarrow u=8\,ms^{-1}$