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  4. A boy standing on road has to hold umbrella at 30° with vertical to keep the rain away. He throws umbrella and starts running at 10 km / hr he finds that rain drops are hitting his head vertically. The speed of raindrops w.r.t. ground is

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Q. A boy standing on road has to hold umbrella at $30^{\circ}$ with vertical to keep the rain away. He throws umbrella and starts running at $10 \,km / hr$ he finds that rain drops are hitting his head vertically. The speed of raindrops w.r.t. ground is

Solution:

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$\vec{v}_{R g}=\vec{v}_{R m}+\vec{v}_{m g}$
From geometry $\frac{v_{m g}}{v_{R g}}=\sin 30^{\circ}$
$\frac{10}{v_{R g}}=\sin 30$
$\therefore V_{R g}=10 \times 2=20 \,km / h .$