Question

Two metra trains approach each other on separate but parallel tracks. one has a speed of 90 km/hr, the other 80 km/hr. initially, the two trains are 2.71 km apart. how long will it take the two trains to pass each other?

Answer 1

The trains take 57.4 s to pass each other.

Two trains A and B move towards each other. Let A move along the positive x axis and B along the negative x axis.

therefore,

`v_A=90 km/h\\ v_B=-80 km/h`

The relative velocity of the train A with respect to B is given by,

`v_A_B=v_A-v_B\\ =(90km/h)-(-80km/h)\\ =170km/h`

If the train B is assumed to be at rest, the train A would appear to move towards it with a speed of 170 km/h.

The trains are a distance d = 2.71 km apart.

Since speed is the distance traveled per unit time, the time taken by the trains to cross each other is given by,

`t= (d)/(v_A_B)`

Substitute 2.71 km for d and 170 km/h for
`v_A_B`

`t= (d)/(v_A_B)\\ =(2.71 km)/(170 km/h) \\ =0.01594 h`

Express the time in seconds.

`t=(0.01594h)(3600s/h)=57.39s`

Thus, the trains cross each other in 57.4 s.