Question

A stone is dropped from the top of tall tower and after $1$ second another stone is dropped from a balcony $20$ m below the top. If both the stones reach the ground at the same instant, then height of the tower is:

• A. 51.25 m
• B. 21.25 m
• C. 31.25 m
• D. 3.125 m

Answer 1

The correct option is C 31.25 m

$s_A=\frac{1}{2}g{t}^2=h.....\left(1\right)$
$s_B=\frac{1}{2}g{t}_1^2=h-20....\left(2\right)$
$t_1=t-1$
$\Rightarrow \frac{1}{2}g{t}^2=h,\frac{1}{2}g(t-1{)}^2=h-20$

Putting value of h from (1) in (2)
$\Rightarrow \frac{1}{2}g(t-1{)}^2=\frac{1}{2}g{t}^2-20$
$20=\frac{1}{2}g(t^2-(t-1{)}^2)\Rightarrow 40=g(2t-1)$
$\Rightarrow 2t-1=4$
$t=\frac{5}{2}=2.5sec$
Height, $A=\frac{1}{2}g(2.5{)}^2=31.25$