Rain is falling vertically with a speed of 35 m s^(-1) . A woman rides a bicycle with a speed of12 m s^(-1) in east to west direction. In which direction should she hold her umbrella ?

Rain is falling vertically with a speed of 35 m s^(-1) . A woman rides

1.	Rain is falling vertically with a speed of 35 m s^(-1) . A woman rides a bicycle with a speed of12 m s^(-1) in east to west direction. In which direction should she hold her umbrella ?
Answer» `sin^(-1)((12)/(35))` `cos^(-1)((12)/(35))` `tan^(-1)((12)/(35))` `cot^(-1)((12)/(35))` Solution :The VELOCITY of the RAIN and the wind are represented by the vectors `vecv_(r)` and `vecv_(w)` as shown in the figure. To protect himself from the rainthe boyshould hold his umbrella in the direction of RESULTANT velocity `vecv_(R)` . If `theta` is the angle which REUSLTANT velocity `vecv_(R)` makes with the vertical, then `tan theta = (v_(w))/(v_(r)) = (12)/(35) or theta = tan^(-1) ((12)/(35))`