Rain is falling vertically with a speed of $35 \;m s ^{-1} .$ A woman rides a bicycle with a speed of $12 \;m s ^{-1}$ in east to west direction. What is the direction in which she should hold her umbrella?
Rain is falling vertically with a speed of $35 \;m s ^{-1} .$ A woman rides a bicycle with a speed of $12 \;m s ^{-1}$ in east to west direction. What is the direction in which she should hold her umbrella?
In figure $v _{ r }$ represents the velocity of rain and $v _{ b },$ the velocity of the bicycle, the woman is riding. Both these velocities are with respect to the ground. Since the 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 Figure makes an angle $\theta$ with the vertical. It is given by
$\tan \theta=\frac{v_{b}}{v_{r}}=\frac{12}{35}=0.343$
$\theta \equiv 19^{\circ}$
Therefore, the woman should hold her umbrella at an angle of about $19^{\circ}$ with the vertical towards the west.
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