Question

A human’s higher initial acceleration suggests that a human might outrun a horse over a very short race, but the horse’s higher top speed allows it win a longer race. A simple – but plausible – model for a sprint by a human and a horse uses the following assumptions: The human accelerates at 8.00 m/s2 for 1.40 s then runs at constant speed. A horse accelerates at a more modest 5.60 m/s2 for a longer time of 3.40 s and then continues at constant speed. Say a human and a horse are competing in a 200 m race. The human is given a 100 m head start, so he begins 100 m from the finish line

a) Draw a diagram of this situation, showing the initial position of both the human and the horse, and the finish line. Draw a single ?-axis for both human and horse to describe these positions. Place the origin of your coordinate system at the horse’s original position. Eventually, the human and horse will meet; label the meeting point on your diagram as ?. Also label the displacement of both human and horse on the diagram, using the meeting point as the final position of both.

b) Assuming that both competitors start from rest, find the top speed of both the human and the horse. Also find their positions when they reach this top speed. (Note: For comparisons’ sake, Usain Bolt can achieve a top speed of roughly 12 m/s, while the fastest recorded speed for a racehorse was roughly 19.7 m/s, achieved by Winning Brew in 2008).

c) Find the position ? where they meet. (2) d) Explain how this meeting point shows who wins the race. What value must this position be compared to make this conclusion?

Answer 1

d) from above calculation we can see that human will win the race as the race was expected to finish at x= 200 meter but the horse catches human at x=270m