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relative velocity

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the rain is falling down vertically shold a man who is running hold umberalla vertically or in tilted posiotion

Why would you hold it tilted to one side if the rain is coming from above?

In the man's rest frame the rain has a horizontal component to its velocity, so the man should tilt his umbrella at an angle.

In the man's rest frame the rain has a horizontal component to its velocity,

Can you really assume that? I'd think that if the rain is falling straight down, with no wind (vertically), it would fall from straight above.

Can you really assume that? I'd think that if the rain is falling straight down, with no wind (vertically), it would fall from straight above.

 

I didn't make any assumptions. From the rest frame of the ground, the man is running horizontally relative to the rain. In the man's rest frame the rain is therefore falling with a horizontal component relative to the man.

A crap, I missed the whole running bit! Twice! Sorry, I take it all back.

Edited by pwagen

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