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 ? if not, guess the correct relation.

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

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 ? if not, guess the correct relation.
Answer» 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)`