I have been confused on this concept for a while - suppose a boy is going from east towards west with some velocity on a bicycle and rain is falling in a vertical downwards direction.
Then, if we have to calculate the angle of an umbrella you'd need to stop yourself getting wet, we consider the relative velocity - subtract velocity of bicycle from velocity of rain because the boy will perceive the velocity of rain differently than an observer and thus adjust it with an angle say A.
That's ok, but does an observer standing on the ground measure that angle differently? We can say they will percieve/measure velocities or distances differently but then they have to do it with angle too otherwise if the observer and the boy perceive only velocity differently and angle the same, the final real outcome will not be same - yet it should be.
So is the point about angle true? Additionally, even if the boy is cycling with a velocity, rain will not change its direction - thus it will fall only vertically downwards. Therefore whatever be boy's (and thus umbrella's) velocity is, it has to counter the same vertically downwards rain with vertically upwards umbrella so how can it change (the angle) in answers (answers state a slant angle not just plain ninety degree)?
And the last question is: How can we solve this(angle calculation) in ground frame?