Motion in One Dimension
11.0 Rain problem
11.0 Rain problem
In rain problem, we come across following three terms.
${\overrightarrow v _R}:$ Velocity of river
${\overrightarrow v _M}:$ Velocity of man
${\overrightarrow v _{RM}}:$ Velocity of rain wrt man
${\overrightarrow v _{RM}}$ is the velocity of the rain which man will observe. Therefore the man will keep his umbrella in the direction of ${\overrightarrow v _{RM}}$ so that he does not get wet.
Mathematically, $${\overrightarrow v _{RM}} = {\overrightarrow v _R} - {\overrightarrow v _M}$$$${\overrightarrow v _R} = {\overrightarrow v _{RM}} + {\overrightarrow v _M}$$
$${v_R} = \sqrt {v_M^2 + v_{RM}^2 + 2{v_M}{v_{RM}}\cos \theta } $$
