A man walking 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 relation has a correct limit : as `vtoo, thetato0`, 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 you, guess the correct relation.

Explanation

tan `theta` must be dimensionless . The correct formula is tan`theta = v//v.` where v. is the speed of rainfall.