Virtually its impossible for a human to reach a point B from a point A travelling a distance X miles!!! But then, how do we reach our travel destinations before the eternal destiny?
Let us try an example now:
You are asked to travel from a point A to point B separated by a distance of X miles.
Let us assume that every day you travel onhalf the leftover distance.
Hence your total travelled distance can be expressed by this series:
Travelled distance after n days= X/2 + X/4 + X/8 + ......+ X/2^n
(Note: Even after n days still a half distance will be left which you travelled in the 'n' th step)
Yet we reach destinations!!!!
So, in real life when you travel keeping this in mind, moving onehalf the distance leftover every time, when will you reach the destination ? please mathematically prove your answer!
2006-11-01 00:35:56 · 10 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
i know a good mathematical riddle, but i wont even bother telling it here, you example has nothing to do with your question, your assumption is false, people dont do that.
2006-11-01 00:39:06 · answer #1 · answered by tomhale138 6 · 0⤊ 1⤋
Yeah, if you actually could move only half the remaining distance each time, you'd never make it. But after a few moves, you are dealing with such small distances that if you move at all, you are going to go much further than you should, and reach your destination.
For example, let's say you want to go 1 meter. After 4 moves, the distance to travel for the 5th move would be 0.03125 m or 3.125 cm. That is a little more than an inch. Keep giong a few more times. The 8th move you make would only be about 3.9 mm. The 10th move would be about 0.98 mm.
Now, how are you going to realistically move your foot 0.98 mm? If you tried, you'd most likely move much further than that. So, eventually you would make it to your 1 meter destination.
Of course, if you WERE able to move exactly the distance needed each time, you would never make it. As n goes to infinity, you asymptotically near X.
2006-11-01 00:49:30 · answer #2 · answered by Jared Z 3 · 0⤊ 0⤋
May i know which person in his/her right mind would walk let sae 1 metre a day when he/her is 2 metres from the destination?
Why not try some philosopher's paradox?
This philospher (whose name eludes me) thought about this. If Achilles (the fastest runner in Greek Mythology) and a tortoise was to race, with the turtle starting perhaps 100 metres before him, how can Achilles catch up with the tortoise? (Provided the race was perhaps 10 miles, but tt's nt the point)
Here's the paradox. The race starts and the positions as such:
|___________________________|___________
A***********************************T***************
For Achilles to reach the position of the turtle, he takes time t.
However, in this time t, the turtle must have moved, perhaps 5 metres.
For Achilles to reach this new position of the turtle 5 metres away, he takes a certain amount of time and again the turtle moves lets say 3 metres. (just an example. i noe its inproportionate)
So do u see his paradox?
2006-11-01 02:10:06 · answer #3 · answered by luv_phy 3 · 0⤊ 0⤋
You will also never be hit by a bullet if you move away from it because :
If the bullet is fired from a distance of X from you and travels at a speed that is n times faster than you, by the time it gets to where you were when it was fired , you have already managed to move away a distance of n/X . When it has moved that distance , again you have moved the n'th part of it. You will always manage to move the n'th part of the distance travelled by the bullet ,therefore it will never reach you
2006-11-01 00:51:14 · answer #4 · answered by mindtelepathy 5 · 0⤊ 0⤋
The series X/2 + X/4 + X/8 + ......+ X/2^n converges to x. so you complete the travel and reach the destination.
Through choosing large enough number of terms of the series ya could get as near to x as you desire. So what's the problem?
just race up.
2006-11-01 00:41:29 · answer #5 · answered by Anonymous · 0⤊ 0⤋
Your math is not wrong, but your assumption is. You cannot put in an assumption into a mathematical equation unless it has no effect on the outcome. Assumptions are for the testing of theory only.
By assuming the travel of half the remaining distance, you change the outcome by definition.
2006-11-01 00:45:54 · answer #6 · answered by Marvinator 7 · 0⤊ 0⤋
but you DONT move like that
People dont move half the distance remainging for each unit of time, this is the classic hunter/arrow puzzle.
If you do move in this wa you will not reach the destination but your position will converge to B over a period of infinity.
The proof is incredibly simple and quite boring so I wont bother with it. Sorry. Have a go though.
2006-11-01 00:42:00 · answer #7 · answered by Stuart T 3 · 0⤊ 0⤋
The question you presented here is applicable if we talk about point mass or a point object only, but I don't think you can apply it for your practical life. And yes if u try your question by assuming that u r a point mass then u might be correct.
2006-11-01 01:24:13 · answer #8 · answered by Napster 2 · 0⤊ 0⤋
You assume that you travel the half of the left over distance.
If you do this the n you are completely right.
But in reality you dont travel like this.
2006-11-01 01:36:18 · answer #9 · answered by gjmb1960 7 · 0⤊ 0⤋
Look up Zeno's paradox on the internet
2006-11-01 00:42:09 · answer #10 · answered by bob h 3 · 0⤊ 0⤋