Red Ball Blue Ball

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At time t=0 a red ball is projected from the origin and travels along the line y = mx at constant speed 2. At the same moment a blue ball is dropped from the point (4, 4) and travels down the line x = 4 at constant speed 1.

(a) The problem is to find the value of m (the slope of the red line) that will produce a direct collision of the two balls. Use the Pythagorean Theorem to find a quadratic equation that m must satisfy.

(b) Construct a Desmos animation that you can use to check your answer in (a). Your animation should have two sliders, an m-slider that changes the slope of the red line and a T-slider that moves the balls. You need to design these so that whatever you choose for m, the T-slider will move the red ball at speed 2. This turns out to be a bit challenging and needs careful thinking. You will be given a warm-up exercise to prepare you.