Suppose a cheetah is dashing due north at a rate of 30 m/s toward a popular watering hole, and a misguided gazelle is running due east toward the same spot at a rate of 20 m/s. The cheetah begins from a distance of 120 m, while the gazelle begins from a distance of 80 m. Find equations for the position y(t) of the cheetah, x(t) for the position of gazelle, and the distance r(t) between them, and use it to find the rate of change of the distance between them at t = 0, t = 2, and t = 4.
The method of implicit differentiation is often applied to related rates problems involving distances.