Question

Tinku dropped a stone into a very deep well. He hears the sound 6.53 s after he dropped the stone. Find the depth of the well. Take acceleration due to gravity, $g=10\frac{m}{s^2}$ and $v_{sound}=340\frac{m}{s}$.

• A. 180 m
• B. 100 m
• C. 90 m
• D. 220 m

Answer 1

The correct option is A

180 m

Initial velocity, u = 0

$T_1$ = time taken by the stone to reach depth D when it is thrown

$T_2$ = time taken by sound to reach the surface

Using second equation of motion, $D=\frac{1}{2}\times 10\times T_1^2$

$T_1=\sqrt{2\times \frac{D}{10}}$

Now, $T_2=\frac{D}{340}$

As per the question, $\sqrt{\frac{D}{5}}+\frac{D}{340}=6.53$

Solving we get, D =180 m.