Register to reply 
Optimization problem with a round lake 
Share this thread: 
#19
Nov2812, 09:09 PM

P: 126

The rowing distance is about 3.46.



#20
Nov2812, 09:25 PM

P: 126

The arc length is 2.09.



#21
Nov2812, 09:28 PM

P: 126

It would take her over two hours to row and walk. So she should row, which would take 2 hours.



#22
Nov2912, 01:46 AM

Homework
Sci Advisor
HW Helper
Thanks
P: 12,463

If you had set up your equation correctly, and rowing the whole way was the quickest route, then there would be a minima in your equation for that situation. There wasn't  instead the minima for the equation gave a slower route that the slowest possible path (see below)  therefore, your equation is set up incorrectly. If she rowed the whole way, then, yes: she would take ##R/u=4/2## or 2hr to get there. This is the slowest route of the ones available. For instance: if she walked the whole way, then she would take ##\pi R/v = 2\pi/4 = \pi/2## or 1.57 hr to get there ... so, of the two choices she should walk  surely? However, there may still be some advantage in rowing some of the way. Your calculation is simply wrong. I am sorry  considering that you will not answer questions, will not follow advise, and will not show your reasoning, I cannot help you. Good luck. 


#23
Nov2912, 02:37 AM

Sci Advisor
HW Helper
Thanks
P: 4,958

RGV 


#24
Nov3012, 02:54 PM

P: 126

I got the same answer as regards to rowing and walking times. I figured out that the chord AB is approximately 1 unit or 1 mile away from the point O and the radius is 2 miles. So the chord is 2[itex]\sqrt{r^{2}d^{2}}[/itex] with d being the distance of the chord from point O. The answer for the chord length is 2[itex]\sqrt{3}[/itex] which equals about 3.46. I divided this by 2 and it came out to be 1.73 hours of rowing.



#25
Nov3012, 03:08 PM

P: 126

I then took 2 arcsin of (cL/2Ra). cL is chord length and Ra is radius and ended up with [itex]\frac{2}{3}[/itex]∏. This is the arc length. I then divided this by 4 and it came out to be about 0.52.



#26
Nov3012, 03:10 PM

P: 126

I agree that walking is the fastest route.



#27
Nov3012, 05:14 PM

Homework
Sci Advisor
HW Helper
Thanks
P: 12,463

You are right though  making x the distance from O to the center of the chord (if that is what you did) is an interesting way of doing it. (I messed up my description before  thanks Ray.) 


Register to reply 
Related Discussions  
During the winter months of Lake Michigan and the bottom of the lake?(freezing point)  Introductory Physics Homework  4  
Recent witness says Bear Lake monster 'is still alive and lurking' :Salt Lake Tribune  General Discussion  0 