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?Here is the image:-

  • $\begingroup$ Welcome to Stack Exchange, I think you could help yourself out here if you were to draw a diagram of sorts - you have some ideas about relative velocities and reference frames that I think you need to "test" to help you understand your question better $\endgroup$ – Alex Robinson Oct 10 '19 at 11:08
  • $\begingroup$ @Alex I have edited this! $\endgroup$ – Nikhil Sharma Oct 10 '19 at 11:37
  • $\begingroup$ Also, try the experiment yourself! Go for a walk in the rain with an umbrella, on a day with no wind. You will need to tilt the umbrella, and the faster you walk or run, the greater is the tilt angle needed to keep the rain off you. $\endgroup$ – PM 2Ring Oct 10 '19 at 11:38
  • $\begingroup$ @PM 2Ring how this problem can be solved from ground reference? I mean you can subtract those velocities from pov of relative velocity concept but what about ground frame? To solve this from ground frame, you kinda have to subtract vectors-opposite from what we do(if bicycle speed is zero and wind is blowing then we add). So how that normalizes(addition of negative)? $\endgroup$ – Nikhil Sharma Oct 10 '19 at 11:44

For a moment forget about the boy and even the angle of the umbrella. Instead, think about the “rain shadow” cast by the umbrella. In the frame of the ground, what does that shadow look like?

At some moment, the umbrella blocks a bit of rain. In the next moment that shadow falls straight down, but the umbrella has moved west a little so now it blocks a bit of rain a little to the west. In the next moment the first bit of shadow falls even further straight down and the second bit of shadow falls straight down a little west and now the umbrella blocks a bit of rain even further west.

Hopefully, you see how the motion of the umbrella leads to the shadow being diagonal in this frame, even though the rain falls vertically. Then it is clear that in this frame the boy must also hold the umbrella at an angle in order to place himself in the rain shadow of the umbrella. Thus both frames are consistent with each other.

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  • $\begingroup$ But why would umbrella move west(even a little)? It is to be hold straight up all the time. $\endgroup$ – Nikhil Sharma Oct 12 '19 at 7:05
  • $\begingroup$ The boy is holding the umbrella while moving west. It has to move west with him unless he drops it. Regardless of the angle it is held, it must move west at the same speed as the boy $\endgroup$ – Dale Oct 12 '19 at 11:06
  • $\begingroup$ but umbrella doesn't have "rain shadow" because rain is falling all over umbrella. $\endgroup$ – Nikhil Sharma Oct 12 '19 at 11:17
  • $\begingroup$ Of course it has a “rain shadow” that is its whole purpose! It’s primary function is specifically to cast a rain shadow so that someone standing in the rain shadow will stay dry! Have you never used an umbrella? I am not having a silly discussion like this. Goodbye. $\endgroup$ – Dale Oct 12 '19 at 11:21
  • $\begingroup$ I didn't mean to annoy you. I simply didn't understand "shadow fall straight down" phrase. I asked only for elaboration because this concept was really difficult for me! $\endgroup$ – Nikhil Sharma Oct 12 '19 at 11:41

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