In the problems, please assume the free-fall acceleration $g=9.80 \mathrm{m} / \mathrm{s}^{2}$ unless a more precise value is given in the problem statement. Ignore air resistance. 56\. (a) If a freestyle swimmer traveled \(1500 \mathrm{m}\) in a time of $14 \mathrm{min} 53 \mathrm{s},$ how fast was his average speed? (b) If the pool was rectangular and \(50 \mathrm{m}\) in length, how does the speed you found compare with his sustained swimming speed of \(1.54 \mathrm{m} / \mathrm{s}\) during one length of the pool after he had been swimming for 10 min? What might account for the difference?

In order to calculate the average speed, first, we need to convert the total time of 14 minutes and 53 seconds to seconds. For this, we multiply the number of minutes by 60 and add the remaining seconds: Total time = (14 min * 60 s/min) + 53 s

Now, we can calculate the average speed using the formula Average speed = Total distance / Total time The distance given is 1500m, and we have the total time in seconds from step 1. Therefore, Average speed = 1500m / Total time

After calculating the average speed, compare it to the provided sustained speed of 1.54 m/s during one length of the pool (50 m) after the swimmer had been swimming for 10 minutes. We shall discuss the possible reasons for the difference.

Lastly, we discuss possible factors that might contribute to the difference in the average speed and the sustained swimming speed of the swimmer. These factors could include the swimmer's initial acceleration, turning time at each end of the pool, and possible slowing down during the race. Let's compute the average speed now: Total time in seconds = (14 * 60) + 53 = 840 + 53 = 893 s Average speed = 1500m / 893s ≈ 1.68 m/s Now, comparing the average speed of 1.68 m/s to the sustained swimming speed of 1.54 m/s, we observe that the average speed is slightly higher. The difference could be attributed to factors such as initial acceleration, turning time at each end of the pool, and the swimmer's pace during different segments of the race. It may also be due to the fact that the swimmer's speed during one length of the pool after 10 minutes of swimming might not fully represent their overall swimming speed throughout the race.