Question

A bug is crawling on the coordinate plane from (5,9) to (-15,-7) at constant
speed one unit per second except in the second quadrant where it travels at 1/2
units per second. What path should the bug take to complete its journey in as
short a time as possible?

i have the answer already, it is from (5,9) to the origin and then to (-15,-7) i just want to know a proof to explain why this is the shortest time

Answer 1

SUBTRACT THE -7 TO -9 AND THE CHANGE OF Y WITH RESPECT TO X

Answer 2

I DON'T HAVE ANYTHING TO ADD BUT I THINK YOUR CAPS LOCK MAY BE BROKEN MINE IS TOO. lol jk mine works fine.

Answer 3

im looking for a proof not how to solve it

Answer 4

wouldn't solving the problem mathematically be a proof? When we prove theories in my Calculus class we prove them by solving a question without them.

Answer 5

even if you solve this problem and get the answer you have no way of proving that this route is true, we are required to discover a proof that will make sure that the path i picked is true

if you can show me how to optimize this problem then yea that could be proof

Answer 6

Shortest path is a straight line, and two straight lines that avoid the second quadrant will have the shortest travel time.

Answer 7

So really what you need to solve is how to prove the shortest path is a straight line.

Answer 8

the shortest path is not the straight line, cause if you draw a straight line connecting the points, it goes through the 2nd quadrant which takes twice amount of time
since i got the answer it is not a straight line it is from (5,9) to (0,0) and then (0,0) to (-15,-7) i need a proof on why that is the fastest path

Answer 9

Right, that's why I said two straight lines. To avoid the second quadrant.

Answer 10

right and i mentioned earlier in the description that i have the answer already i just needed a proof

Answer 11

ahhh this is the issue neither of you are correct their will be certain amount of time that is worth heading not in a straight line to minimize the time in the second quadrant but if you avoid it completely that could take to much time compared to going partially through the second quadrant. It is a tricky question that I have seen before I just wished for the life of me I remembered how to do it.

Answer 12

no avoiding the 2nd quadrant is the answer, to be honest i have a proof, but what i really wanted was a detailed proof of this

Answer 13

cause im not 100% sure that my proof works

Answer 14

Have you had your answer confirmed by the marker/a teacher/someone other than yourself?

Answer 15

yes, i had several people say that that is the answer

Answer 16

http://www.lecture-notes.co.uk/susskind/classical-mechanics/lecture-2/shortest-distance-between-two-points/

Answer 17

sorry im 100% sure i understand what exactly this link is telling me, if you can show me how to prove this problem using the technique you metioned in the link, then that would be helpful

Answer 18

I just found the link, that's not my work. But I checked out 3-4 of the google results and this looked the most straight forward. But, no I haven't understood the proof myself. That, and it's bedtime here on the east coast. Hope you figure out the proof though.

Answer 19

its ok thanks for your help