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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 ?

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The direction in which boy should hold his umbrealla is opposite to resultant velocity of rain and wind. Let vertically up be y-axis and west to east be x -axis.
Now, ` vecv_(R) = - 30hatj , vecv_(w)jj = - 15 hatj`
The resultant velocity of rain and wind is
`vecv_(R) + vecv_(w) = - 30 hatj - 15 hatj `
From , the figure , ` tan tehta = 15/20 = 1/2`
` Rightarrow theta = tan^(-1) (1/2)`
So, the boy should hold his umbrealla inclined at an angle ` tan^(-1)(1/2)` with vertically ,towards east.
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