Rain is falling down vertically. To a man walking on the road, velocity of rain appears to be 1.5 times his velocity. Then to protect himself from rain, he holds his umbrella at an angle (theta) to the vertical such that tan (theta) =
The relative velocity of rain to man is R-M where R is rain velocity and M is man's velocity.
The Attempt at a Solution
Assume the rain velocity vector is R. We can think it is -rJ. J is a unit vector along y axis. r is the magnitude of rain velocity. The negative sign comes because of the direction of rain - down.
Similarly M = mI where I is unit vector along x axis. The relative velocity of rain to man is R-M = -rJ-mI.
The magnitude of R-M is 1.5m (given).
1.5m = sqrt(r^2+m^2) implies m/r = 2/sqrt(5) = tan(theta).
But the answer stated in the book is the reciprocal i.e. sqrt(5)/2. Who is right?