Rain is falling vertically with a speed of $20\;ms^{-1}$. A person is running in rain (from east) with a velocity of $5 ms^{-1}$ and a wind is blowing with speed of $15ms ^{-1}$ (from west).The angle with the vertical at which the person should hold his umbrella is

Question

\[(a)\;\tan ^{-1}\bigg(\frac{1}{2}\bigg)\quad (b)\;\tan ^{-1}\bigg(\frac{1}{3}\bigg) \quad (c)\;\tan ^{-1}\bigg(\frac{4}{5}\bigg) \quad (d)\;\tan ^{-1}(3)\]