A man walking briskly in rain with speed upsilon must slant his umbrella forward making an angle(with the vertical). A student derives the following relation between theta and upsilonn : tan theta = upsilon and checks that the relation has a correct limits : as upsilon rarr 0, theta rarr 0. as expected. (we are assuming there is no strong wind and that the rain vertically for a stationary man). Do you think this relation can be correct ? ifnot, guess the correct relation.

A man walking briskly in rain with speed upsilon must slant his umbrel

1.	A man walking briskly in rain with speed upsilon must slant his umbrella forward making an angle(with the vertical). A student derives the following relation between theta and upsilonn : tan theta = upsilon and checks that the relation has a correct limits : as upsilon rarr 0, theta rarr 0. as expected. (we are assuming there is no strong wind and that the rain vertically for a stationary man). Do you think this relation can be correct ? ifnot, guess the correct relation.
Answer» Solution :The RELATION `tan theta = upsilon has a CORRECT limit, as upsilon rarr 0 , theta rarr0.` 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)`