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

The relation `tan theta = upsilon has a correct limit, as upsilon rarr 0 , theta rarr 0.`
However, `RHS = tan theta = [M^0 L^0 T] and LHS = upsilon = [M^0 L^1 T^(-1)].`
Therefore, the relation is not correct dimensionally.
As we go through unit 3 of the book, we shall find that the correct relation is tan `theta = (upsilon^2)/(rg)`