Two trains, initially separated by distance d, travel toward each other at a slo

Question

Two trains, initially separated by distance d, travel toward each other at a slow speed vt . A man in a Jeep is driving on the trail next to the train tracks at a fast speed vj (assume the speed of the Jeep is always vj ). He starts adjacent to the front of one train and drives until he reaches the front of the other train. He then quickly turns around drives back until he reaches the front of the first train again. He then quickly turns around, inexplicably repeating the process until the trains meet. Show that the distance travelled by the Jeep is given by D =vjd /2vt

Explanation / Answer

let t is the time taken for the trains to meet.

so, time taken, t = distance travelled/relative velocity of trains

t = d/(2*vt)

distance traveled by the jeep during this time,

D = vj*t

= vj*d/(2*vt)

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