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Question

Two trains each having a speed of 30 kmph are headed at each other on the same straight track. A bird that can fly at 60 kmph flies off from one train when they are 60 km apart and heads directly for the other train. On reaching the other train, it flies directly back to the first and so forth. How many trips can the bird make from one train to the other before the crash. Also find the total distance that the bird travels.

A
trips=, distance=60 km
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B
trips=30, distance=30 km
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C
trips=5, distance=60 km
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D
trips=5, distance=30 km
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Solution

The correct option is A trips=, distance=60 km
vrel=30+30=60 kmph (for trains)
drel=60 km
Time taken for the trains to meet =6060=1 hr
Relative velocity between the bird and train
=60+30=90 kmph
For 1st trip t=6090=23 hrs
Separation between the trains after 1st trip (d1)=dvrelt1=6060×23=20 km
For 2nd trip t2=2090=232 hrs
d2=2029×60=203 km
t3=203(90)=233 hrs
tn=23n
Hence total time T=t1+t2++tn
=2[13+132+133++13n]=23[1(13)n][113]
=113n
But T=1 hrs1=113n13n=0
n=
Total distance travelled by the bird =vt=60×1=60 km

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