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An observed stands at a point $ P $, one unit away from a track. Two runners start at a point $ S $ in the figure and run along the track. One runner runs three times as fast as the other. Find the maximum value of the observer's angle of sight $ \theta $ between the runners.

$\frac{\pi}{6}$

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Campbell University

University of Nottingham

Idaho State University

okay for this question, we know we're trying to find the maximum value of the angle of sight, which is data. Okay, The first thing we know is that three tea over one is equivalent to cheap plus chan data over one minus T Jim Data, which essentially tells us that Tim Theta is duty over one plus three t squared. This gives us the derivative said equal to zero gives us t is squirt of three over three. Therefore, we know there's an absolute minimum at this point squirt of three over three, as I've written over here, therefore, we know that inverse tangent is pi over sex, which is our solution.