Rain is falling vertically downwards at a velocity 9 ~ms ⁻¹ . And wind starts blowing at a speed of 4 ~ms ⁻¹ in the west to east direction. In which direction should the girl hold her umbrella to protect herself from the rain?

Step-by-step solution

Let the velocity of rain be v _ r = -9 j ms ⁻¹ , where j is the unit vector in the upward vertical direction. The velocity of the wind is v _ w = 4 i ms ⁻¹ , where i is the unit vector in the west to east direction. The velocity of the rain with respect to the girl (who is assumed to be stationary) is v _ rg = v _ r - v _ w = -4 i - 9 j ms ⁻¹ . To protect herself from the rain, the girl must hold the umbrella in the direction of the relative velocity of the rain, which is v _ rg = -4 i - 9 j . The angle that the um