math and physics question

[nwicole]

A fly is resting on the front of a train that is hurtling forward at 60 kilometers per hour. On the same track, 300 kilometers straight ahead, another train is hurtling towards the first train at 60 kilometers per hour. At that moment, when the trains are 300 km apart, the fly takes off at 90 km per hour. He continually flies back and forth between the trains, flying just above the track and instantaneously turning around when he reaches a train.

What is the total distance traveled by the fly before the two trains crash together, squishing the fly between them in the process? Explain your answer.

 

[Ishuda]

A fly is resting on the front of a train that is hurtling forward at 60 kilometers per hour. On the same track, 300 kilometers straight ahead, another train is hurtling towards the first train at 60 kilometers per hour. At that moment, when the trains are 300 km apart, the fly takes off at 90 km per hour. He continually flies back and forth between the trains, flying just above the track and instantaneously turning around when he reaches a train.

What is the total distance traveled by the fly before the two trains crash together, squishing the fly between them in the process? Explain your answer.

Do we need to also compute relativistic effects or can we just use the simple add the velocities and see how long it will take for the trains to collide.

 

[Deleted member 4993]

Do we need to also compute relativistic effects or can we just use the simple add the velocities and see how long it will take for the trains to collide.

It is said that Von Neuman had solved the problem adding infinite sequence of distance traveled by the fly - in 30 seconds.

 

[Ishuda]

It is said that Von Neuman had solved the problem adding infinite sequence of distance traveled by the fly - in 30 seconds.

A simple geometric series.

 

[HallsofIvy]

That's an old "chestnut" or joke. The story goes that some one posed this problem to Von Neuman who thought for a moment, then gave the correct answer. The person who posed it chuckled and said "Some people try do that by summing the series of distances". At which Von Neumann looked at him in puzzlement and said "That's what I did!"

 

[stapel]

A fly is resting on the front of a train that is hurtling forward at 60 kilometers per hour. On the same track, 300 kilometers straight ahead, another train is hurtling towards the first train at 60 kilometers per hour. At that moment, when the trains are 300 km apart, the fly takes off at 90 km per hour. He continually flies back and forth between the trains, flying just above the track and instantaneously turning around when he reaches a train.

What is the total distance traveled by the fly before the two trains crash together, squishing the fly between them in the process? Explain your answer.

To learn how to set up and solve "distance" word problems, try here. Then note that you only need to find the time:

If the two trains are approaching each other at 60 and 60 kph, then at what speed is the distance between them closing? (In other words, if one train weren't moving, how fast would the other one need to move for the distance to close at the same rate?) At that rate, how long will it take the trains to meet? Given the fly's speed, how far will the fly have travelled in that amount of time?