Question 187 of 308

A girl standing on road holds her umbrella at $45^{\circ}$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt{2}km{h}^{-1}$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is

A$30km{h}^{-1}$B$\dfrac{25}{\sqrt{2}}km{h}^{-1}$C$\dfrac{30}{\sqrt{2}}km{h}^{-1}$D$25km{h}^{-1}$

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Answer: (C) $\dfrac{30}{\sqrt{2}}km{h}^{-1}$

${\vec{v}}_{rg}={\vec{v}}_{r}-{\vec{v}}_{g}$

From the above diagram, velocity of the raindrop wrt ground will be,
$\left|{\vec{v}}_{r}\right|=\sqrt{{\left(15\sqrt{2}\right)}^{2}+{\left(15\sqrt{2}\right)}^{2}}=30km{h}^{-1}$
And velocity of the raindrop wrt the moving girl will be,
$\left|{\vec{v}}_{rg}\right|=15\sqrt{2}=\dfrac{30}{\sqrt{2}}km{h}^{-1}$