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Question:

Rain is falling vertically with velocity (2root3)m/s. if air starts to blow horizontally at 2m/s then What will be the speed of rain and direction to an observer?

Answer:

vector v_r = -2(3)^1/2 j

vector v_a = 2 i

Relative velocity of rain with respect to air = v_r– v_a = sqrt[(-2(3)^1/2]² + 2²) = 4(3) + 4 = 16 m/s

Direction of observer = tan θ = v_a / v_r = 2/ -2(3)^1/2 = -1/(3)^1/2

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