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    
 
						

							
when the separation between two trains is 60km, after which the sum of distance travelled by each train is equal to 60km.
S1 + S2 =60   ( s=ut + 1/2at^2) sice the speec is constat so a=0 )
30t + 30t = 60
t=1hr this is the time taken by the trains to collide after the 60km separation.
so, distance travelled by bird in this time interval is 60x1=60km. ( v of bird=60)