Two electric trains travel in the same direction along the same track at a uniform speed of 72 km/h , maintaining a separation of 2.4 km . Both trains sound brief whistles simultaneously. At the instant the whistling occurs, a person is located at a perpendicular distance of 500 m from the track and is equidistant from the two trains. Given that the speed of sound in air is 340 m/s and the original frequency of both

Step-by-step solution

Speed of the trains, v_s = 72 km/h = 72 5 18 = 20 m/s . The separation between the two trains is 2.4 km = 2400 m . Since the person is equidistant from both trains at the instant of whistling, the distance along the track from the person's projection to each train is 2400 2 = 1200 m . The perpendicular distance of the person from the track is 500 m . The straight-line distance from each train to the person is: d = 1200^2 + 500^2 = 1300 m Let be the angle between the track and the line joining the train to the perso