A man wlaking 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 relations has a correct limit : as `v rarr 0, theta rarr 0` , as expected . (We are assuming there is no string wing and that the rains falls vertically for a stationary man). Do you think this relation can be correct ? If not, guess at the correct relation .

Explanation

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