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Optimization problem with a round lake 
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#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

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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

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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

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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.) 


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