Rain is fallinf vertically with a speed of 35 m s^(-1). A women rides a bicycle with a speed of 12ms ^(-1) in east to west dicrection . Whatis the direction in which she should hold her umbrella ?

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

1.	Rain is fallinf vertically with a speed of 35 m s^(-1). A women rides a bicycle with a speed of 12ms ^(-1) in east to west dicrection . Whatis the direction in which she should hold her umbrella ?
Answer» Solution :In Fig . 4.16 `v_(r )` represents the velocity of rain and `v_(b)` , the velocity of the bicycle , the women is riding . Boththese velocities are with RESPECT to the GROUND . Sincethe woman is riding a bicycle , the velocity of rain as experienced by her is the velocity of rain relative to the velocity of the bicycle she is riding . That is `v_(rb) =v_(r )-v_(b)`This relative velocity vector as shown in Fig . 4.16 makes an angle `theta` with the vertical . It is GIVEN by `tantheta=(v_(b))/(v_(r))=(12)/(35)=0.343``tantheta=(v_(b))/(v_(r))=(12)/(35)=0.343` Or , `theta~=19^(@)` Therefore , the women should hold her umbrella at an angle of about `19^(@)` with the vertical towards the WEST .