A bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has a speed of 18 m/h while the other has the speed of 27km/h. The bird starts moving from first car towards the other and is moving with the speed of 36km/h and when the two cars were separted by 36 km. What is the total distance covered by the bird? What is the total displacement of the bird?

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2015-09-16T03:32:02+05:30

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The total time duration For the two cars to meet
       = total distance/relative velocity
       = 36 km / (18+27)  kmph = 4/5  hours

In this duration, the 1st car travels :  4/5 hr* 18 kmph = 14.4 km
That is the meeting point.

In this time period, the bird could travel : 4/5 hr * 36 kmph = 28.8 km
 This is the total distance travelled by the bird. ..

displacement from starting position will be = distance of the meeting point from the starting point of 1st car:  14.4 km
 
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alternately,

Bird meets car2, after   t = 36/63 hr = 4/7 hr
At this time distance between car1 and bird/car2:  4/7 *(36-18)=72/7 km

Bird meets car1 after :  (72/7) / 54 hrs = 4/21 hrs  ie., at total time 16/21 hrs total
The distance between bird/car1 and car2 is now: 36 - (16/21)*45 = 12/7 km

Bird meets car2 now after  (12/7)  km/63 kmph = 4/147 hrs  at time total = 116/147 hrs
Now the distance between Bird/Car2 and car1 will be: 36 - 116/147 * 45 = 72/147 km

Bird meets car1 now after:  (72/147)  / 54 =4 / 441 hrs   at total time: 352/441 hrs
Now distance between car1/Bird and car2 is: 36 - 352/441 * 45 = 12 /147

The shuttling durations of bird are: 4/7, 4/21, 4/147, 4/441,
Distance  36, 12/7 , 12/147

Total of the shuttling times = 4/7 + 4/147 + ... + 4/21 + 4/441+...
       = (4/7) / [1 - 1/21] + (4/21) / [1 - 1/21]
         = 3 / 5 hrs.  +  1/5 hrs  = 4/5 hours

Total distance travelled by bird:  4/5 hrs * 36 kmph = 28.8 km

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