Q 2.25: A man walking briskly in rain with speed v must slant his umbrella forward making an angle  with the vertical. A student derives the following relation between and  and checks that the relation has a correct limit: as , 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.

The derived formula  is dimensionally incorrect.

We know, Trigonometric functions are dimensionless.

Hence , [ ] =

and [v] = .

To make it dimensionally correct, we can divide v by (where  is the speed of rain)

Thus, L.H.S and R.H.S are both dimensionless and hence dimensionally satisfied.

The new formula is :

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