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.
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The derived formula
is dimensionally incorrect.
We know, Trigonometric functions are dimensionless.
Hence , [
] = 
and [v] =
.
Thus, L.H.S and R.H.S are both dimensionless and hence dimensionally satisfied.
The new formula is :