Question

It was a rainy day in Bangalore. Rohit was sitting beside the window when he saw a lightning. He started his stopwatch. He found that after 22 seconds of lightning its roaring was heard. Calculate the height of the clouds (approximately) which caused this lightning. Given,
Speed of light = $3\times {10}^8\frac{m}{s}$ and Speed of sound = $340\frac{m}{s}$.

• A. 10km
• B. 8.5km
• C. 7.5km
• D. 5km

Answer 1

The correct option is C

7.5km

Here, we are considering two motions. One is the motion of light and another one is the motion of sound caused by clouds. We are given that the speed of light is $3\times {10}^8\frac{m}{s}$and speed of sound $340\frac{m}{s}$. We are also given the difference in time of these two reaching to Rohit. We have to find the height of the clouds.

Let's assume the height of the clouds is = h

then time taken by light will be = $\frac{Distance}{speed}$ = $\frac{h}{3\times {10}^8}$

Similarly, the time taken by sound will be = $\frac{h}{340}$

Difference in time taken by these two = 22 seconds (Given)

$\Rightarrow \frac{h}{340}-\frac{h}{3\times {10}^8}=22$

$\Rightarrow h(\frac{1}{340}-\frac{1}{3\times {10}^8})=22$

The speed of light is too high. So you can assume no time delay in colliding clouds and lightning. Since the time taken for light to travel from clouds to earth is approximately 0. $\frac{1}{3\times {10}^8}$ i.e $\to 0$.

$\Rightarrow \frac{h}{340}=22$

$\Rightarrow h=340\times 22$

So we can say that lightning happened at t = 0, and sound reached our ears at 22s. So height of clouds = 22 x 340 = 7480m ≈ 7.5km.