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Two trains are approaching each other . A mosquito which flies at velocity v flies from one train to another and repeats this process. The two trains are at a distance x. How many complete journeys can mosquito make before the trains crash?

Two trains are approaching each other . A mosquito which flies at velocity v flies from one train to another and repeats this process. The two trains are at a distance x. How many complete journeys can mosquito make before the trains crash?

Grade:11

1 Answers

deepak
84 Points
7 years ago
dude this quetion is first of all absurd cos you never mentioned anything about the velocities of the trains,
but let us assume that the veloctiy of the 1st train is v1 and the velocity of the second train to be v2.
now let us asume the observer is on the train 2 then for the observer the velocity of the train one will be v1+v2
but there are three different cases,
(1) if v1+v2 > v then
the mosquito will never make it to the train two before train one does
(2) if v1+v2 =v
then both the train one and the mosquito will reach the train 2 at the same moment.
so the mosquito will make one complete journey.
(3) if v> v1+v2
then ,
let us think in this way, think that the mosquito reaches the train 2 once and is about to make its way back to train one then by that time train one would have moved by some distance resulting in the reduction of the distance the mosquito has to cover inorder to meet train 1 i.e. for the second complete journey distance to be covered will be lesser than the previous one.
similarly for each journey the distance will be lowered. therefore at some small disatance x the mosquito will make several complete journeys before the trains meet resulting in the answer that the mosquito will make infinite trips before the trains colliede if v>v1+v2.
 
 
hope this proves to be helpful and p.s. its very difficult to find the no of trips made

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