How to Solve rain man Problem | Physics JEE - NEET | Extraclass.com

How to Solve the rain man Problem?
Let us analyze the situation where a man on the ground experiences rainfall.
Say if the man is holding an umbrella and rain starts falling from the vertical direction.
Certainly, his umbrella will save the man from getting wet
But what will happen if the man starts walking?

To answer this correctly, we need to find the velocity of rainfall with respect to man.
The velocity of raindrops with respect to man VRM is given by the relation velocity of rain VR minus velocity of man VM
Let’s consider this XY frame of reference

Since the rain is falling in vertically downward in Y direction let’s say VR vector
And man is moving towards the right along X direction with velocity VM
So minus VM vector would be in the minus X direction
The resultant of the two vectors will be in the direction of the velocity of raindrops with respect to man.
This means that the man will observe that the rain is falling at an angle theta from the vertical where tan theta can be calculated as the ratio of magnitude VM and VR.
So while walking if a man is holding the umbrella in vertical direction and raindrops are hitting at an angle theta with the vertical direction
Then obviously the man will get wet.
So in order to save himself from getting wet, he has to hold the umbrella in the direction of raindrops with respect to man.

All of us hold our umbrella’s similarly at an angle to avoid getting wet intuitively without caring about the physics behind this.
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