Question

The flash of a gun is seen by mass 5 sec before the sound is heard. What is the distance of the gun from the man? (Speed of sound in air is 332m/s).
(A) 66.4m
(B) 1660m
(C) 6.64m
(D) 166m

Answer 1

Hint
We are given time taken by the sound of gun flash to reach a man at some distance. We have to find the distance between man and gun at that moment. We will calculate that distance using speed-time relation.

Complete step by step answer
As we know that the concept of lightning and thunder that we are able to see lightening earlier than thunder is heard. This is because the speed of light is greater compared to the speed of sound.
Similarly; we are able to see the flash of a gun before the sound of flash.
Time taken in between both the speed was just 5 sec as mentioned in the question.
So, $t = 5$ sec
Using Speed - Time relation;
$speed = \dfrac{{dis\tan ce}}{{time}}$ …(1)
Speed tells us the rate at which distance of an object changes or speed is a quantity that determines the distance travelled by an object in a specific time interval.
Or $u = \dfrac{s}{t}$ where, u = speed of sound in air = 332m/sec (given)
s = distance travelled by sound
t = time taken by sound to travel
From (1),
$distance = speed \times time$
$distance = 332 \times 5m =1660m$
Thus, distance of the gun from the observer I.e. man is 1660m.
Hence the correct solution is 1660m, I.e. option (B).

Note
If the speed/time = distance is used then we get option (A) I.e. 66.4m will be the solution. But this is the wrong solution. Symbol s should not be misinterpreted as speed.