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 `v_(r ) and v_(w)` in Fig. 4.7 and are in the direction specified by the problem . Using the rule of vector addition , we see that the resultant of `v_(r )andv_(w)` is R as shown in the figure . The magnitude of R is
`R=sqrt(v_(r)^(2)+v_(w)^(2))=sqrt(35^(2)+12^(2)) "m s"^(-1)=37 " m s "^(-1)`
The direction `theta` that R makes with the vertical is given by
`tantheta=(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 plame at an angle of about `19^(@)` with the vertical towards the east.