11 ms·
1. Feynman explains it best https://www.youtube.com/watch?v=msN87y-iEx0 https://www.youtube.com/watch?v=msN87y-iEx0 3. They approach one another at 30000 mph
by evanb 12y ago
1. Feynman explains it best https://www.youtube.com/watch?v=msN87y-iEx0 https://www.youtube.com/watch?v=msN87y-iEx0
3. They approach one another at 30000 mph = 500 miles per minute, so two minutes before they collide they are 1000 miles apart, and who cares that they start out 1317 miles apart?
8. The balloon rushes forward, and gets pulled toward the inside of the curve. The best reasoning is via the equivalence principle: acceleration and gravity feel the same, and the fact that the balloon is buoyant in air means that it should rush away from whatever direction gravity is pointing.
9. It floats at the same location, by Gauss' theorem.
- JshWright 12y ago> 3. They approach one another at 30000 mph = 500 miles per minute, so two minutes before they collide they are 1000 miles apart, and who cares that they start out 1317 miles apart? It was clearly just a distraction, and apparently an effective one, as the question was "calculate how far apart they are _one_ minute before they collide".
- LanceH 12y agoThe version I heard that truly leads a calculus student down the wrong path is along the lines of: Train a is going 40 mph, train b 60 mph. They are 200 miles apart on the same track, headed directly for each other. There is a bird flying between the two at 100 mph, starting from train a. Each time he reaches a train he turns around and heads back to the other train. How far does the bird travel before he is crushed between the trains?
- anon4 12y agoI don't see what's so hard about that one, it's a simple infinite sum.
- jameshart 12y agoThere's an easier way than an infinite sum.
- Khao 12y ago40mph + 60mph = 100mph, so they will travel for 2 hours before they hit each other. The bird flying at 100 mph for 2 hours will travel 200 miles.
- thesteamboat 12y agoanon4 is referencing one of the tellings of this story where famous scientist [usually Von Neumann] is given this problem as a brainteaser and responds instantly having done it the `hard way'. http://mathforum.org/dr.math/faq/faq.fly.trains.html http://mathforum.org/dr.math/faq/faq.fly.trains.html
- Bill_Dimm 12y ago"...calculate how far apart they are one minute before they collide" So, the answer is 500 miles (not 1000 miles).
- evanb 12y agoAh, on my screen the text wraps right where it says the number of minutes, and my brain parsed the Two from the beginning of the question.