Rain, driven by the wind, falls on a railway compartment with a velocity of 20 m s - 1 , at an angle of 30 ° to the vertical. The train moves, along the direction of wind flow, at a speed of 108 km hr - 1 . The apparent velocity of rain for a person sitting in the train is

Step-by-step solution

Speed of train = 1 0 8 × 5 1 8 = 3 0 m/s Let v ⁡ → R ⁡ and v ⁡ → T ⁡ represent the respective velocities of rain and train. Now, the relative velocity of rain w.r.t person (train) is given by v ⁡ R, T = v ⁡ → R ⁡ - v ⁡ → T ⁡ ⇒ v ⁡ → R ⁡ + - v ⁡ → T ⁡ Let OR → and RT → represent the vectors in magnitude and direction. OT 2 = OR 2 + RT 2 + 2OR × RT cos 120 o = 2 0 2 + 3 0 2 - 2 × 2 0 × 3 0 × 1 2 = 4 0 0 + 9 0 0 - 6 0 0 = 7 0 0 = 7 0 0 m/s