like fishing, napping etc, then he leaves the top of the mountain to come back down the next morning at 5am taking the same path back down and reaches the bottom at 5pm also making whatever stops along the way down, what are the odds that he will be at the exact same spot at the exact same time anywhere along the way as the day before?
2007-03-29 05:29:05 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Physics
He will obviously be it the same places he had been the day before but will it be the exact same time as the day before
2007-03-29 05:45:19 · update #1
The odds are 100%. Set it up as a graph with the x-axis being time running from 5 am to 5 pm, and the y-axis being his progress along the path. The origin is 5:00 a.m. at the base of the path. Graph his climb as location against time. It will start at the origin and run upward and to the right until it gets to the highest y-coordinate on the graph (the top of the path).
Now graph his return trip. That line will start at the top left of the graph at a point on the y-axis corresponding to the top of the path, and at x = 0 (meaning 5:00 a.m.). Now draw his return from there to the point on the x-axis that represents 5:00 p.m. and the base of the path. No matter how you draw the return, it will cross the upward line at some point. Therefore there is at least one point where he's at that point at the same time of day as he was the day before.
Or think of it this way. Make the graph a square ABCD, arranged like this:
AB
CD
with the C at the origin of the x,y graph. C represents 5:00 a.m. at the base of the path, D represents 5:00 p.m. at the base of the path, A represents 5:00 a.m. at the top of the mountain, and B represents 5:00 p.m. at the top of the mountain. His upward hike is a line that runs from C to B. His downward hike is a line that runs from A to D. You can't connect C to B (upward hike) and also connect A to D (downward hike) within the box without having the lines cross at some point.
2007-03-29 05:42:35 · answer #1 · answered by Isaac Laquedem 4 · 0⤊ 0⤋
It would be pretty unlikely. Especially since it doesnt sound like he is on a trail. The best way up is not necessarily the best way down. Also it take about a third less time to go down than it does to go up a mountain.
Oh wait you said he takes the same path. yes 100%. he will cross his own path obviously.
2007-03-29 12:40:36 · answer #2 · answered by sssnole 4 · 0⤊ 0⤋
Zero
I'll take a mulligan. 100%.
An equivalent problem is if a second person begins the descent at the same time as the first person starts the climb, will there be a point where their paths cross?
2007-03-29 12:36:06 · answer #3 · answered by Anonymous · 0⤊ 0⤋
100%
Imagine that is was two different people walking up and down on the sam day. What would be the odds that they would pass each other. 100%
2007-03-29 12:37:18 · answer #4 · answered by Anonymous · 0⤊ 0⤋
If his napping etc is totally random, the probabilty will be infinitely small
2007-03-29 12:34:08 · answer #5 · answered by Gene 7 · 0⤊ 0⤋