Rain is falling vertically with a speed of `35ms^-1`. A woman rides a bicycle with a speed of `12ms^-1` in east to west direction. What is the direction in which she should hold her umbrella?

Explanation

The velocity of the rain and the wind are represented by the vectors Vr and Vw in the figure and are in the direction specified by the problem. Using the rule of vector addition. We see that the resultant of `V_(r)` and `V_(w)` is R as shown in the figure. The magnitude of R is:

The direction `theta` that R makes with the vertical is given by
`tan theta =V_(w)/V_(r) = 12/35 = 0.343` or `theta = tan^(-1)(0.343) = 19^(@)`
Therefore, the boy should hold his umbrella in the vertical plane at an angle of about 19D with the vertical towards the east.