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

Option: 1

\mathrm{30kmh^{-1}}


Option: 2

\mathrm{\frac{25}{\sqrt{2}}kmh^{-1}}


Option: 3

\mathrm{\frac{30}{\sqrt{2}}kmh^{-1}}


Option: 4

\mathrm{25kmh^{-1}}


Answers (1)

best_answer

When girl starts running  \vec{V}_{\text {rain } / \text { Girl }}=\vec{V}_{\text {rain }}-\vec{V}_{\text {Girl }}

              

\mathrm{V_{\text {Girl }}=V_{\text {rain }} \sin 45^{\circ}} \\

\mathrm{15 \sqrt{2}=\operatorname{Vrain} \times \frac{1}{\sqrt{2}}}\\

\mathrm{V_{\text {rain }}=30 \mathrm{~km} / \mathrm{hr}}\\

\mathrm{V_{rain/Girl} = {V_{rain } \cos 45^{\circ}= 30 \cos 45^{\circ}=\frac{30}{\sqrt{2}} \mathrm{km} / \mathrm{hr}}

Hence the correct answer is option 3.

Posted by

Ritika Kankaria

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