Ncert Exercises & Solutions

15.2 A stone dropped from the top of a tower of height 300 m splashes into the water of a pond near the base of the tower. When is the splash heard at the top given that the speed of sound in air is 340 m/sec? $(g = 9.8 m / s^{2})$

It is given in the question that :

Height of the tower, s = 300 m

Acceleration, a = g = 9.8 m / s^{2}

Speed of sound in air = 340 m / s

If the time taken by the stone to strike the water in the pond = t_{1}

Using the second equation of motion :

\begin{array}{l} s = {ut}_{1} + \frac{1}{2} {gt}_{1}^{2} \\ 300 = 0 + \frac{1}{2} \times 9 .8 \times t_{1}^{2} \\ ∴ t_{1} = \sqrt{\frac{300 \times 2}{9 .8}} = 7 .82 s \end{array}

Time taken by the sound to reach the top of the tower, t_{2} = \frac{300}{340} = 0.88 s

Therefore, the time after which the splash is heard,

= 7.82 + 0.88 = 8.7 s

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