Randall D. Knight — Kinematics in One Dimension: Problem Problem_52

A cheetah spots a Thomson’s gazelle, its preferred prey, and leaps into action, quickly accelerating to its top speed of \(30\text{ m/s}\), the highest of any land animal. However, a cheetah can maintain this extreme speed for only \(15\text{ s}\) before having to let up. The cheetah is \(170\text{ m}\) from the gazelle as it reaches top speed, and the gazelle sees the cheetah at just this instant. With negligible reaction time, the gazelle heads directly away from the cheetah, accelerating at \(4.6\text{ m/s}^2\) for \(5.0\text{ s}\), then running at constant speed. Does the gazelle escape? If so, by what distance is the gazelle in front when the cheetah gives up?