Two trains, each having speed 30 km/h, are headed at each other on the same straight track. A bird that can fly 60 km/h flies off the front of one train when they are 60 km apart. On reaching the other train, the bird directly flies back to the first train and so forth. What is the total distance the bird travels before the train collides?

Ans: Total time interval for the birds motion = time taken for the trains to collide ie t = initial seperation / velocity of approach = 60/ 2(30) = 1 hour therfore, distance covered by bird = t.v = 1.60 = 60 kms

hiii

when the train is 60 km apart bird flies

time taken by it to travel to other train 

60t + 30t = 60

t = 2/3 hr

when bird reach othe train  distance between two trains = 20 km

time taken by it to travel to first train

60t + 30t = 20

t = 2/9 hr

this process will continue n times

so distance moved by bird = 60 x 2/3 +60 x 2/3² ................................60 x 2/3ⁿ

= 60 x 2/3 (1 + 1/3 + 1/3² ......................1/3ⁿ )

^{= 80/3 km    ....................          Ans}