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Rain is falling vertically with a speed ...

Rain is falling vertically with a speed of 30 m/s. wind starts blowing after some time with a speed of 15 m/s in east to west direction. In which direction should a boy waiting at a bus hold his umbrella ?

Text Solution

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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)=37 ms^(-1)`
The direction 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 an angle of about `19^(@)` with the vertical towards the east.
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