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Model: One-Dimensional Motion with Constant Velocity applies to each person separately. Depending upon how you visualize the problem, the model may have to be applied twice to the runner (person 1). We will explore this detail suggest two possible methods to deal with this issue in the Approach.
Approach: This problem stretches the definition of One-Dimensional Motion with Constant Velocity. Even if we assume the path is perfectly straight, the runner must reverse direction at the summit, and so it would seem that person 1's velocity changes its mathematical sign within the problem. We will suggest two possible methods to deal with this issue.
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One way to be sure that each person has constant velocity in is to split the problem is to shift the initial time. into two parts. The point of division is when person 1 reaches the summit and turns around. If we set up a one-dimensional coordinate system as shown below, then during the first part of the problem person 1 is