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  • A person walking at a rate of 3km/hr, the rain falls vertically.when he increase his speed to 6km/hr it appears to meet him at an angle of 30⁰.what is the speed of rain

A person walking at a rate of 3km/hr, the rain falls vertically.when he increases his speed to 6km/hr it appears to meet him at an angle of 30 degrees.What is the speed of rain

Answers (1)

Let the velocity of rain be xi + yj

Speed of the rain = \\\sqrt{x^2+y^2}\\\\

the velocity of man = 3i

The relative velocity between man and rain in case one is vertical

That is 

\\v_{rm}=(v_r-v_m)=(xi+yj)-3i\\

x=3 since relative velocity has only the vertical component.

Case 2

v_{rm}=(3i+yj)-6i=-3i+yj

Since the rain is coming at 30 degrees the angle between the relative velocity of rain and man is 150 degree

Therefore

\\\frac{y}{-3}=\frac{1}{\sqrt{3}}\\\\y=\sqrt{3}

Therefore

\\v_r=3i+\sqrt{3}j\\\\|v_r|=\sqrt{9+3}=\sqrt{12}=2\sqrt{3}m/s

Posted by

Safeer PP

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