Rain is falling vertically with a speed of 12√3m/s. A woman rides a bicycle with a speed of 12m/s in East to West direction. What is the velocity of rain relative to the woman? ( Eastward and upward are positive x-axis and y-axis respectively)
A
(12√3^i+12^j)m/s
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B
(12√3^i+12√3^j)m/s
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C
(12^i+12√3^j)m/s
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D
(12^i−12√3^j)m/s
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Solution
The correct option is D(12^i−12√3^j)m/s
Let West to East direction be positive x – axis and upward direction be positive y – axis. Therefore, Velocity of rain fall w.r.t ground →vR=−12√3^jm/s Velocity of bicycle w.r.t. ground →vW=−12^im/s So, velocity of rain w.r.t bicycle, →vRW=→vR−→vW=−12√3^j−(−12^i)=(12^i−12√3^j)m/s