Rain is falling vertically with a speed of $35 \;m s ^{-1} .$ Winds starts blowing after sometime with a speed of $12 \;m s ^{-1}$ in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella?
Rain is falling vertically with a speed of $35 \;m s ^{-1} .$ Winds starts blowing after sometime with a speed of $12 \;m s ^{-1}$ in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella?
Answer The velocity of the rain and the wind are represented by the vectors $v _{ r }$ and $v _{ w }$ in 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
$R=\sqrt{v_{r}^{2}+v_{w}^{2}}=\sqrt{35^{2}+12^{2}} m s ^{-1}=37 m s ^{-1}$
The direction $\theta$ that $R$ makes with the vertical is given by
$\tan \theta=\frac{v_{w}}{v_{r}}=\frac{12}{35}=0.343$
Or, $\quad \theta=\tan ^{-1}(0.343)=19^{\circ}$
Therefore, the boy should hold his umbrella in the vertical plane at an angle of about $19^{\circ}$ with the vertical towards the east.
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