# 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.

Answers (1)

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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