Rain, driven by the wind, falls on a railway compartment with a...

\text{Speed$of$train} = 1 0 8 \times \dfrac{5}{1 8} = 3 0 \text{m/s} Let${\overset{→}{v }}_{R }$\text{and}${\overset{→}{v }}_{T }$ represent the respective velocities of rain and train.Now, the relative velocity of rain w.r.t person (train) is given by ${v }_{R, T} = {\overset{→}{v }}_{R } - {\overset{→}{v }}_{T } ⇒ {\overset{→}{v }}_{R } +$\left(- {\overset{→}{v }}_{T }\right)Let $\overset{→}{OR} \text{and} \overset{→}{RT} represent$ the vectors in magnitude and direction.OT2 = OR2 + RT2 + 2OR × RT \cos 120o= 2 {0}^{2} + 3 {0}^{2} - 2 \times2 0 \times3 0 \times$\dfrac{1}{2} = 4 0 0 + 9 0 0 - 6 0 0 = 7 0 0 = \sqrt{7 0 0} \text{m/s} \text{\text{ and } }$