A drone is flying due west, a little above the train, with a speed of 10 ~m / s . A 270 meter long train is moving due east at a speed of 20 ~m / s . The time taken by the drone to cross the train is

Step-by-step solution

Let the velocity of the drone be v _ d = -10 i m/s (due west). Let the velocity of the train be v _ t = 20 i m/s (due east). The relative velocity of the drone with respect to the train is v _ dt = v _ d - v _ t = -10 i - 20 i = -30 i m/s . The magnitude of the relative velocity is | v _ dt | = 30 m/s . The length of the train is L = 270 m . The time taken by the drone to cross the train is t = L | v _ dt | = 270 30 = 9 s . Answer: 9 s