Rain is falling vertically with a speed of $30\; m /s$. A woman rides a bicycle with a speed of $10\; m/ s$ in the north to south direction. What is the direction in which she should hold her umbrella ?
Rain is falling vertically with a speed of $30\; m /s$. A woman rides a bicycle with a speed of $10\; m/ s$ in the north to south direction. What is the direction in which she should hold her umbrella ?
The described situation is shown in the given figure.
Here,
$v_{ c }=$ Velocity of the cyclist
$v_{ r }=$ Velocity of falling rain
In order to protect herself from the rain, the woman must hold her umbrella in the direction of the relative velocity ( $v$ ) of the rain with respect to the woman. $v=v_{r}+\left(-v_{c}\right)$
$=30+(-10)=20 \,m / s$
$\tan \theta=\frac{v_{ c }}{v_{ r }}=\frac{10}{30}$
$\theta=\tan ^{-1}\left(\frac{1}{3}\right)$
$=\tan ^{-1}(0.333) \approx 18^{\circ}$
Hence, the woman must hold the umbrella toward the south, at an angle of nearly $18^{\circ}$ with the vertical.
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- [KVPY 2012]