1oh yeah..i forgot....it should be 'infinite' no of trips....but let not me give the solution for this part...let the others try too!!
This is a tricky ques found in most books.But i enjoyed solvin it so here it is. Two trains each having a speed of 30km/hr are heading towards each other on the same straight track.A bird that can fly at 60km/hr flies off one train when they are 60km apart and heads directly for the other train.On reaching the other train it flies directly back to the first and so forth.Find (a)how many trips can the bird make from one train to the other before the trains collide? (b)what is the total distance travelled by the bird? Answer will be given later if no one solves it
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5 Answers
1hi,
The bird flies at a constant
speed for the entire time that the trains travel until colliding. The distance the bird travels is thus
d = v t =60km/h
We need to compute the time that the trains run before colliding. By symmetry, we can argue
that the trains will collide in the middle, at 30 km. The time to collision is easy to compute,it’s
just the time for either time to travel 30 km, which is 1 hour. Now that we know how long the
trains will run, we can see that the distance the bird will travel is 60 km.....
I think this is the answer....
1Yes the distamce travelled by the bird will be 60km but that is the simple part of the question.What will be the answer to part (a)of the question?
1
1Final Solution:
Velocity of bird: 60km/hr
Let the bird begin to fly frm 1st train(A)to the 2nd train(B).velocity of bird w.r.t to B=90km/hr.so to cross a dist of 60km time taken is t1=60/90=2/3hr. By this time the dist between two trains is s1=(60-2/3*60)=(13)60km
Now the bird flies towards A with velocity 90km/hr w.r.t train A, time t2=(13)(6090)=(13)(23)hr.So now the distance between two trains= s2=(1360-132360)=(13)2 60km
The 3rd time distance between the two trains will be,
s3=(13)3 60km. Thus sn=(13)n 60km. So the number of flights made by the bird is infinity.
Time taken for the trains to collide= 6030+30=1 hr .During this time the bird flies a distance of 60km.
keep questioning!!!