Question

The velocity of sound in air is 330m/s. Convert this speed in km/hr. How much time does it take to cover 99km.
[a] 1188km/hr, 5min
[b] 1188km/hr, 4min
[c] 1180km/hr, 5min
[d] 1180km/hr, 4min.

Answer 1

Hint: Using the fact that $s=vt$, where s is the distance covered, v is the speed and t is the time taken, determine the distance covered by the sound in 1 hour. Convert this distance in km and hence find the speed of the sound in km/hr. Using $t=\dfrac{s}{v}$, where s is the distance covered, v is the speed and t is the time taken determine the time taken by sound to cover 99Km.

Complete step by step answer:
We have $1hr=3600s$
We know that the distance(s) covered in time (t) when speed is v is given by $s=vt$
Hence, the distance covered by the sound in 1 hour is $330\times 3600m$
We know that 1km = 1000m.
Hence the distance covered by the sound in 1hour is $\dfrac{330\times 3600}{1000}=1188km$
Hence the speed of the sound is $1188km/hr$
Now, we know that $t=\dfrac{s}{v}$ where s is the distance travelled, t is the time taken and v is the speed.
Hence the time taken to cover 99km by the sound is $\dfrac{99}{1188}hr=\dfrac{1}{12}hr=5\min $
Hence the time taken by the sound to cover 99 km is 5min.

So, the correct answer is “Option A”.

Note: [1] Conversion trick. For converting km/hr to m/s multiply by $\dfrac{5}{18}$ and for converting m/s into km/hr multiply by $\dfrac{18}{5}$
Using the above trick the speed of the sound in km/hr is $\dfrac{18}{5}\times 330=1188$km/hr which is the same as obtained above. Hence proceeding similarly as above the time taken by the sound to cover 99 km is 5min.
Hence option [a] is correct.