Rain is falling vertically with a speed of 35 ms^(-1) . Windsstarts blowing aftersometime with a speed of 12 ms in east to west direction . In which direction should a boywaiting at a bus stop holdhis umbrella ?

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

1.	Rain is falling vertically with a speed of 35 ms^(-1) . Windsstarts blowing aftersometime with a speed of 12 ms in east to west direction . In which direction should a boywaiting at a bus stop holdhis umbrella ?
Answer» Solution :The velocity of the RAIN and the windare represented by the vectors `v_(r ) and v_(w)` in Fig. 4.7and arein the direction specified by the PROBLEM . Usingthe ruleof 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 , theboy should hold his umbrella in thevertical plame at an angle of about`19^(@)` with the vertical towards the east.