Rain is falling vertically with a speed of 35 ms^(-1). Winds starts blowing after sometime with a speed of 12ms^(-1) in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella ?

Rain is falling vertically with a speed of 35 ms^(-1). Winds starts bl

1.	Rain is falling vertically with a speed of 35 ms^(-1). Winds starts blowing after sometime with a speed of 12ms^(-1) in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella ?
Answer» Solution :The VELOCITY of the rain and the wind are represented by the vectors `v_(r)` and `v_(w)` 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 the angle of about `19^(@)` with the vertical towards the east.