Question

Rain is falling vertically downwards. To a man running east-wards, the rain will appear to be coming from:
A) East
B) West
C) Northeast
D) Southeast

Answer 1

In order to solve this question, the knowledge of relative velocity is important. As, velocity is defined as speed with direction and also is a vector quantity, so direction is an important part of velocity. Here keep in mind that the rain is falling downwards, which will make the velocity of rain zero and hence it would be easier to solve the question.

Complete step by step answer:
It is given in the question that the man is running towards the east.
Let the velocity of the running man be represented as ${V_{man}}$
Let the velocity of the rain be represented as ${V_{rain}}$.
The relative horizontal velocity of the rain with respect to the man will be given by
${V_{rain,man}} = {V_{rain}} - {V_{man}}$
It is given in the question that the rain is falling downwards.
Hence, we have ${V_{rain}} = 0$.
Putting the value of ${V_{rain}} = 0$ in the equation ${V_{rain,man}} = {V_{rain}} - {V_{man}}$ we have,
${V_{rain,man}} = 0 - {V_{man}}$
The above expression gives us, ${V_{rain,man}} = - {V_{man}}$
The negative sign here represents the opposite direction.
As the man is moving in the east direction as per the question so the velocity of rain is west with respect to man.
So, velocity of the rain with respect to man is west, hence the rain will appear to come from east for man.

So, option A is the correct option.

Note: Relative velocity of an object can be described as the velocity of an object B in the rest frame of another object A. Velocity can be described as speed with direction. Relative velocity between two objects can be in the form of magnitude as well as direction as given in this question.