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A man walking briskly in rain with speed...

A man walking briskly in rain with speed u must slant his umbrella forward making an angle q with the vertical. A student derives the following relation between q and v : tan q = v and checks that the relation has a correct limit : as `v to 0, q to 0`, as expected. (We are assuming there is no strong wind and that the rain falls vertically for a stationary man). Do you think this relation can be correct ? If not, guess the correct relation.

Text Solution

Verified by Experts

The relation `tantheta=v` has a correct limit,
as `v to 0, theta to 0`.
However, `RHS=tanthetta=[M^(0)L^(0)T^(0)]` and L.H.S `=v=[M^(0)L^(1)T^(-1)]`
Therefore, the relation is not correct dimensionally.
We shall find the correct relation is
`tantheta=v^(2)/(rg)`
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