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#### bergausstein

##### Active member

- Jul 30, 2013

- 191

can you help solve the first part of the question? thanks!

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- Thread starter
- #1

- Jul 30, 2013

- 191

can you help solve the first part of the question? thanks!

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\(\displaystyle x(t)=\cos\left(\frac{2\pi}{T}t \right)\)

\(\displaystyle y(t)=\sin\left(\frac{2\pi}{T}t \right)\)

where $T$ is the period of their motion, i.e., the time (in minutes) it takes for them to complete one circuit of the track.

Then equate the respective coordinates of both runners, and take the first positive solution for $t$.

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- Jul 30, 2013

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Let $C$ be the circumference of the track, and using distance = rate times time, and subscripting the faster runner's parameters with a 1 and the slower runner with a 2. We may use the fact that when the faster runner laps the slower runner, his distance ran will be one more circumference than the slower runner, and write:

\(\displaystyle d_1=d_2+C\)

Use $d=vt$:

\(\displaystyle v_1t=v_2t+C\)

What are the velocities of the two runners?