A rain is falling with a speed of 35m/s.Wind starts blowing after sometime with a speed of 12 m/s in east to west direction. In which direction should the boy hold his umbrella to protect himself?

To the boy , the rain will appear to fall in the direction of the resultant of the rain and wind.

Let ? be the angle which the resultant velocity subtends with the vertical.

Then, tan ? = velocity of wind/ velocity of rain = 12 / 30 = 2 /5

or, ? = tan^-1 (2/5)

 The boy should hold the umbrella at an angle  ? = tan^-1 (2/5) south of vertical.