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

According to principle of homogenity of dimensional equations, Dimensions of `L.H.S. =` Dimensions of `R.H.S.`
Here, `v =tan theta`
i.e., `[L^(1) T^(-1)] =` dimensionless, which is incorrect
Correcting the `L.H.S.` we. Get
`v//u=tan theta`, where u is velocity of rain.