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

1.	Rain is falling vertically with a speed of 35ms^(-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. `R=sqrt(v_(r)^(2)+v_(w)^(2)) = sqrt(35^(2)+12^(2))MS^(-1) = 37ms^(-1)` The direction `theta` that R makes the vertically 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 plane at an angle of about `19^(@)` with the vertically towards the east.