Question
If $${V_r}$$ is the velocity of rain falling vertically and $${V_m}$$ is the velocity of a man walking on a level road, and $$\theta $$ is the angle with vertical at which he should hold the umbrella to protect himself, than the relative velocity of rain w.r.t. the man is given by:
A.
$${V_{rm}} = \sqrt {V_r^2 + V_m^2 + 2{V_r}{V_m}\cos \theta } $$
B.
$${V_{rm}} = \sqrt {V_r^2 + V_m^2 - 2{V_r}{V_m}\cos \theta } $$
C.
$${V_{rm}} = \sqrt {V_r^2 + V_m^2} $$
D.
$${V_{rm}} = \sqrt {V_r^2 - V_m^2} $$
Answer :
$${V_{rm}} = \sqrt {V_r^2 + V_m^2} $$
Solution :
According to pythagorus theorem
$${V_{rm}} = \sqrt {V_r^2 + V_m^2} $$
According to pythagorus theorem
$${V_{rm}} = \sqrt {V_r^2 + V_m^2} $$
