Problem 54670. Solve an ODE: precocious pair’s porcine pursuit

Created by ChrisR

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 237.45px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 118.725px; transform-origin: 407px 118.725px; vertical-align: baseline; "><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 236.133px 7.79167px; transform-origin: 236.133px 7.79167px; unicode-bidi: normal; ">In our previous encounters with Matilda and Labrun, the scintillating siblings <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/53004">collected candy wrappers</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; ">, <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/51451">amused others with card tricks</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 17.5px 7.79167px; transform-origin: 17.5px 7.79167px; unicode-bidi: normal; ">, and <a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/51251">found interesting relations involving house numbers on their street</a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 3.88333px 7.79167px; transform-origin: 3.88333px 7.79167px; unicode-bidi: normal; ">. </div><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 266.292px 7.79167px; transform-origin: 266.292px 7.79167px; unicode-bidi: normal; ">But now their pet pig has run away, and the pair must catch her! They start a distance d<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 104.233px 7.79167px; transform-origin: 104.233px 7.79167px; unicode-bidi: normal; "> away from the pig, which runs at speed V<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 336.5px 7.79167px; transform-origin: 336.5px 7.79167px; unicode-bidi: normal; "> in a direction perpendicular to the line connecting the initial positions of the pig and the siblings. Matilda and Labrun run at speed v<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 197.208px 7.79167px; transform-origin: 197.208px 7.79167px; unicode-bidi: normal; ">, always in a direction pointing at the current position of the pig. </div><div style="block-size: 63.45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.725px; text-align: left; transform-origin: 384px 31.725px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 122.383px 7.79167px; transform-origin: 122.383px 7.79167px; unicode-bidi: normal; ">Write a function that takes the distance d<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 254.775px 7.79167px; transform-origin: 254.775px 7.79167px; unicode-bidi: normal; "> and the two speeds and returns the time required for Matilda and Labrun to catch their pet. Return <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 7.79167px; transform-origin: 11.55px 7.79167px; unicode-bidi: normal; ">Inf<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 311.95px 7.79167px; transform-origin: 311.95px 7.79167px; unicode-bidi: normal; "> if the pair will not catch the pig, and please ignore the impracticality of reporting times to the nearest microsecond. </div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 133.033px 7.79167px; transform-origin: 133.033px 7.79167px; unicode-bidi: normal; ">This problem is adapted from a problem in <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 194.492px 7.79167px; transform-origin: 194.492px 7.79167px; unicode-bidi: normal; ">Advanced Mathematical Methods for Scientists and Engineers <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 47.4583px 7.79167px; transform-origin: 47.4583px 7.79167px; unicode-bidi: normal; ">by Bender and Orzsag.</div></div></div>

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4 Solutions
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Last Solution submitted on Jun 02, 2022

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Solution 8450135

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ChrisR on 26 May 2022

The simplicity of the final answer to this problem does not really reflect the work required to get it.

Tim on 28 May 2022

From dimensional analysis you can see that the solution has to be of the form t=(d/V)*f(v/V), and someone might be able to figure out function f from the data points, and save the trouble of solving the differential equation.

ChrisR on 28 May 2022

Sure, but where's the fun in that? :-)

ChrisR on 28 May 2022

On the other hand, that approach is a good example of what a teacher described as being "lazy and smart"--that is, using cleverness to avoid work. Anyone interested in dimensional analysis might check out CP 46031.

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Problem 54670. Solve an ODE: precocious pair’s porcine pursuit

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Problem 54670. Solve an ODE: precocious pair’s porcine pursuit

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