Question

A straight train track running north-south on a flat and otherwise featureless plain meets a straight road running east-west at right angles. As the last car of a train heading north at 100 km/h passes this intersection, a drone is flying west directly over the road at 200 km/h is 1 km east of the intersection. At this instant, the drones controller decides to have it chase the train and thereafter keeps the drone headed directly towards the last car of the train until it catches up. If the train and drone maintain their speeds of 100 km/h and 200 km/h, how far from the crossing does the drone catch up with the last car of the train?

Answer 1

As drone's velocity is directed towards the train, it's velocity becomes $(-200 i+100j)m/s$ where north represents positive y-axis and east represents positive x-axis.

Now, as the initial horizontal distance is 1km. It takes the drone $1/200hr.$ to cover this distance(y-component of velocity does not affect the motion in x-direction and vice versa).

In this $1/200hr.$ the train and the drone travel $(1/200)*100km=0.5km$ in the positive y-direction.

Thus, the drone and train meet each other at a distance of 0.5km from the intersection point.