Question

Human vs Horse. 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 would allow it to 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 7.50 m/s2 for 1.40 s then runs at constant speed. A horse accelerates at a more modest 5.80 m/s2 for a longer time of 3.20 s and then continues at constant speed. a) Assuming that both competitors start from rest, find the top speed of both the human and the horse. Also find how much distance they would cover while accelerating to this top speed. (6) (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). b) Say these two are competing in a 200 m race, but the human is given a 100 m head start (so really, the human is only running a 100 m race). Determine who wins by finding the time required for each to run the race. (4)

Answer 1

To find the top speed of the human and the horse, we first need to calculate the distance covered during the acceleration phase.

For the human:

Acceleration = 7.50 m/s^2

Time = 1.40 s

Using the equation: Distance = (1/2) * acceleration * time^2

Distance = (1/2) * 7.50 * (1.40)^2

For the horse:

Acceleration = 5.80 m/s^2

Time = 3.20 s

Distance = (1/2) * 5.80 * (3.20)^2

Now, let's calculate the top speed for both the human and the horse.

The human's top speed is reached after the acceleration phase, so the distance covered during acceleration is equal to the distance covered at the top speed.

For the human:

Distance = top speed * time at constant speed

Distance = top speed * (200 m - distance covered during acceleration)

Using the calculated distance covered during acceleration and the above equation, we can solve for the top speed of the human.

For the horse:

Distance = top speed * time at constant speed

Distance = top speed * 200 m

Using the calculated distance covered during acceleration and the above equation, we can solve for the top speed of the horse.

To determine who wins the 200 m race with a 100 m head start for the human, we need to find the time required for each to run the race.

For the human:

Time = (200 m - 100 m) / top speed of the human

For the horse:

Time = 200 m / top speed of the horse

By comparing the times for both the human and the horse, we can determine the winner of the race.

It's important to note that the calculations above are based on the given assumptions and may not reflect real-world scenarios.

Step-by-step explanation: