How far will the cheetah need to run to catch the horse?

Question

 A horse runs by a cheetah at a top speed of 21 m/s. A cheetah notices the horse and stands up after 1 s. The cheetah then immediately speeds up with a constant acceleration of 9 m/s² to catch the horse. How far will the cheetah need to run to catch the horse?

Answer 1

d_H = 21t with displacement of the horse, d_H, in meters and the time, t, in seconds.

d_C = (1/2)*9*(t-1)² where the displacement of the cheetah, d_C, in meters is calculated for constant acceleration, but starting after 1 second of delay.

The problem becomes a matter of equating d_H and d_C at the critical time, t^*. Once you have the time when they have moved the same d, you can input into either equation in order to find the displacement. Equating the displacements will lead to a quadratic equation in t. Use quadratic formula.

Good Luck!