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

Relation obtained by student, `tantheta=v`
Dimensions of left hand side of equation `M^(0)L^(0)T^(0)` because it.s a trignometric ratio.
and dimensions of right side are `M^(0)L^(1)T^(-1)` Hence, given relation is not true.
True relation should be `tantheta=(v)/(u)`. where u= initial speed or velocity.