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 $v \rightarrow 0, \theta \rightarrow 0$, 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 not, guess the correct relation.