A man moving in rain holds his umbrella inclined to the vertical even though the rain drops are falling vertically downwards. Why?

Explanation

Let us consider a person moving horizontally with velocity `vec(V)_(m)` . Let rain falls vertically with velocity `vec(V)_(R)` . An umbrella is held to avoid the rain. Then the relative velocity of the rain with respect to the person is ,
`vec(V) _(RM)= vec(V)_(R)- vec(V)_(M)`
Its magnitude is given by
`V_(RM) = sqrt(vec(V)_(R)^(2)+vec(V)_(M)^(2))`
Its direction is given by `theta = tan^(-1) ((V_(M))/(V_(R)))` With the vertical . In order to sane himself from the rain, he should hold an umbrella at an angle `theta` with the vertical.