Question

What will be the answer?

Answer 1

(i) An infinite number of trips, each shorter than the previous one.
(ii) 100 km.

Explanation:

Measuring the time from when the trains are `100`km apart, they will travel for `1` hour before they crash at the midpoint.

If the bird flies at a constant speed of `100`km/h, reversing its direction of travel when it meets a train, then it will have travelled a total of `100`km in that hour.

At each point of time before the hour is up, when the bird reaches a train, the other train will be at a non-zero distance. When the bird has (instantaneously!) reversed its direction of travel, it has a velocity with respect to the track twice that of the train it has just encountered. Therefore it will reach the other train before the crash.

So the bird will make an infinite number of shorter and shorter trips, totalling `100`km.

Answer 2

(i) I think it is `oo` number of trips. Each time bird flies from one train to the other, the distance traveled by it becomes smaller.

(ii) Time taken by the trains to crash`=`Total time taken by the bird in motion

`"Time taken by trains to crash"= "Initial separation" / "Relative speed"`

`= 100/ (50+50) = 1\ h`

`:.` Distance traveled by bird `= "Speed of bird"xx"Time"`

`= 100xx1 =100\ km`