Two train are approaching each other with speed of 10m/sec and 20 m/sec respectively. As of now, distance between them is 300 meter. One bird start from train A and move to Train B repeatedly. Speed of bird is 1 m/sec. How much distance bird cover before train collide?
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But an engineering solution might be to say that the fly stops going back and forth when the distance between the trains is equal to the fly's length, say 1 cm. After all the work he's done, the poor guy starts getting smashed after this time. The distance between the trains could be expressed as, D(t)=300−30t, where D and t are in units of meters and seconds, respectively. To avoid the infinite result, we can calculate the trips the fly makes up until he starts getting smashed, Tsmash=300−110030=9.999667 seconds. Seems like the number of round trips the fly makes (N) can be approximated as:
N=12∫Tsmash0dtD(t)v
where v=50 m/s is the fly's speed and the 1/2 multiplier is to make N equate to 'round trips'. This computes to
N=˙8.59.
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