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For a man running horizontally along east at speed of 4 km/hr, the rain appears to fall vertically. If he doubles his speed the rain appears to hit him at an angle at 30° with vertical. The original speed and direction of rain will be

Option: 1

4 km/hr, 30° with vertical towards east


Option: 2

  4 km/hr, 30° with vertical towards west


Option: 3

  8 km/hr, 30° with vertical towards east


Option: 4

  8 km/hr, 30° with vertical towards west


Answers (1)

best_answer

Answer (3)

Let \vec{v}_{r}=a\hat{i}-b\hat{j}

\vec{v}_{rm}=\left ( a-4 \right )\hat{i}-b\hat{j}\left ( \text {in first condition} \right )

a-4=0

a=4\; km/hr

\vec{v}_{rm}=\left ( a-8 \right )\hat{i}-b\hat{j}\left ( \text {in second condition} \right )

\vec{v}_{rm}=\left ( 4-8 \right )\hat{i}-b\hat{j}

         =-4\hat{i}-b\hat{j}

\tan 30^{o}=\frac{4}{b}

\frac{1}{\sqrt{3}}=\frac{4}{b}

b=4\sqrt{3}

\vec{v}_{rg}=4\hat{i}-4\sqrt{3}\hat{j}

Posted by

Ritika Kankaria

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