Question

If you hear a gunshot 2 sec after it is fired, how far away from the gun are you? (speed of sound in air = $ 330{m \mathord{\left/
 {\vphantom {m s}} \right.} s} $ ).

Answer 1

Hint: This question can be solved by applying the distance-speed equation. The units of the values must be kept in mind and stated after each quantity for better understanding.

Formula Used: The formulae used in the solution are given here.
$ s = vt $ where $ s $ is the distance, $ v $ is the speed and $ t $ is the time taken by a body to cover that distance at $ v $ speed.

Complete step by step solution:
Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only magnitude and no direction.
Mathematically, when the distance to be travelled is $ s $ , and the time taken to cover that distance is $ t $ , then the speed of the body must be $ v $ , where $ v = \dfrac{s}{t} $ .
It has been given that, it takes 2 seconds for the sound of the gun shot to reach the observer when the speed of sound in air is given as $ 330{m \mathord{\left/
 {\vphantom {m s}} \right.} s} $ .
Thus, the distance between the source of sound, that is the gun, and the observer is given by the product of the speed of sound in air and the time taken is 2 seconds.
Thus, assigning the values $ v = 330{m \mathord{\left/
 {\vphantom {m s}} \right.} s} $ and $ t = 2s $ , the value of $ s $ can be calculated.
Since, $ s = vt $ where $ s $ is the distance, $ v $ is the speed and $ t $ is the time taken by a body to cover that distance at $ v $ speed
 $ s = 330 \times 2 = 660m. $
Thus the distance between gun and observer must be 660 metres.

Note:
For the measurement of speed in vehicles, speedometers are used. To measure the distance covered odometers are used. Speed can also be calculated with the help of a graph. The Distance-time graph helps in understanding the speed of an object.
There are four types of speed and they are:
-Uniform speed: An object is said to be in uniform speed when the object covers equal distance in equal time intervals.
-Variable speed: An object is said to be in variable speed when the object covers a different distance at equal intervals of times.
-Average speed: Average speed is defined as the uniform speed which is given by the ratio of total distance travelled by an object to the total time taken by the object.
Instantaneous speed: When an object is moving with variable speed, then the speed of that object at any instant of time is known as instantaneous speed.