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

Explanation

Because LHS is dimensionless
where RHS `=v=[M^(0)LT^(-1)]`
Dimension of LHS is not equal to dimension of RHS
To make the relation correct
We should have `tan theta= (v)/(u)`
Here u is speed of rainfall.