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 :