To a stationary man, rain appears to be falling at his back at an angle 30 o with the vertical. As he starts moving forward with a speed of 0 .5 m s - 1 , he finds that rain falls vertically. The speed of rain with respect to stationary man is

Question

To a stationary man, rain appears to be falling at his back at an angle 30 o with the vertical. As he starts moving forward with a speed of 0 .5 m s - 1 , he finds that rain falls vertically. The speed of rain with respect to stationary man is, 0 .5 m s - 1, 1 m s - 1, 3 2 m s - 1, 1 3 m s - 1

MARKS App · Accepted Answer

For stationary person For running person Speed of rain with respect to a stationary man = ν v → = v sin 30 o i ^ − v cos 30 o j ^ The velocity of rain with respect to man, v → R M = v → R − v → M = ( v sin 30 o i ^ − v cos 30 o j ^ ) − ( 0.5 i ^ ) Since V → R M is vertically downward, its x -component will become zero. ∴ v sin 30 o − 0.5 = 0 ⇒ v = 0.5 sin 30 o = 1 m s - 1

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