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repository:triathlete_s_dilemma [2021/01/27 18:26] porcaro1 [Activity] |
repository:triathlete_s_dilemma [2021/02/16 23:53] (current) porcaro1 [See Also] |
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| ===Handout=== | ===Handout=== | ||
| ** Triathlete's Dilemma ** | ** Triathlete's Dilemma ** | ||
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| + | {{ :repository:triathlete.png?nolink&600|}} | ||
| You are a triathlete in the water and you need to get to your bike parked in a rack at a specific location on the shore in the shortest amount of time possible. You can run faster than you can swim. Do you swim directly to the shore, then run to your bike? Do you swim to a point closer to your bike, then run? How do you solve this dilemma? Here are the specific parameters: | You are a triathlete in the water and you need to get to your bike parked in a rack at a specific location on the shore in the shortest amount of time possible. You can run faster than you can swim. Do you swim directly to the shore, then run to your bike? Do you swim to a point closer to your bike, then run? How do you solve this dilemma? Here are the specific parameters: | ||
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| ===Handout=== | ===Handout=== | ||
| Our first modifications to the code are defining the variables "target" (line 22), and "final" (line 24). This represents at which x-coordinate you reach the shore and the x-coordinate of the bike rack, respectively. We add the variable "dt" (line 23) which is a miniscule increment in time, and used later in our while loop. We then create equations for the "swimtime" and "runtime" variables (lines 25 & 26); these equations are just a rearranged form of the Pythagorean Theorem solved for the length of the hypotenuse and divided by the swim speed and run speed variables—remember that distance divided by speed is time. Finally, the limits of the while loop are defined (line 35) and the swim time and run time equations are reentered (lines 37 & 38). Looking at the output graph, the optimal x-coordinate along the shore line is equal to -24.5. | Our first modifications to the code are defining the variables "target" (line 22), and "final" (line 24). This represents at which x-coordinate you reach the shore and the x-coordinate of the bike rack, respectively. We add the variable "dt" (line 23) which is a miniscule increment in time, and used later in our while loop. We then create equations for the "swimtime" and "runtime" variables (lines 25 & 26); these equations are just a rearranged form of the Pythagorean Theorem solved for the length of the hypotenuse and divided by the swim speed and run speed variables—remember that distance divided by speed is time. Finally, the limits of the while loop are defined (line 35) and the swim time and run time equations are reentered (lines 37 & 38). Looking at the output graph, the optimal x-coordinate along the shore line is equal to -24.5. | ||
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| + | {{ :repository:triathlete_graph.png?nolink&600 |}} | ||
| Extension Solutions: | Extension Solutions: | ||
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| ===Code=== | ===Code=== | ||
| - | <code Python [enable_line_numbers="true", highlight_lines_extra=""]> | + | <code Python [enable_line_numbers="true", highlight_lines_extra="22,23,24,25,26,35,37,38"]> |
| GlowScript 2.8 VPython | GlowScript 2.8 VPython | ||
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| ---- | ---- | ||
| ====See Also==== | ====See Also==== | ||
| - | * | + | *[[inner_tube_river_crossing | Inner Tube River Crossing]] |
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