Question

The average speed of a track and field runner is 10.6 m/s. This is approximately 23.7 mph. In track and field, there are many different events: Sprints 100, 200, and 400 meters; middle distance 800 and 1500 meters; long distance 3000, 5000 and 10,000 meters; hurdles 100 and 400 meters; and relays 4x100, and 4x400 meters. A four-person relay team is running a 4x100 meter race. This means that each runner sprints a distance of 100 meters before handing off the baton to the next runner. During practice, the coach timed each runner multiple times and came up with an average velocity for each one which included the time it took to hand off or start from the beginning. The first runner has an average velocity of 10.6 m/s. The second had an average of 10.5 m/s. The third had an average of 9.9 m/s. The final runner, often called the anchor, has an average velocity of 10.8 m/s. Given this information how long should it take each runner to run their part of the relay? How long should it take for the team to complete the entire relay race?

Answer 1

The time for each runner to run their part of a 4x100 meter relay is calculated using the formula time = distance ÷ velocity, which yields 9.43 seconds, 9.52 seconds, 10.10 seconds, and 9.26 seconds for the first, second, third, and fourth runners, respectively. The total time for the team to complete the relay race is 38.31 seconds.

Step-by-step explanation:

To calculate the time it takes for each runner to complete their leg of the 4x100 meter relay, we use the formula time = distance ÷ velocity. Since each runner covers 100 meters, we divide this distance by their average velocity.

• First runner: 100 m ÷ 10.6 m/s = 9.43 seconds
• Second runner: 100 m ÷ 10.5 m/s = 9.52 seconds
• Third runner: 100 m ÷ 9.9 m/s = 10.10 seconds
• Fourth runner (anchor): 100 m ÷ 10.8 m/s = 9.26 seconds

The total time for the team to complete the entire relay race is the sum of the times for each runner. Therefore, the team's total time is 9.43 s + 9.52 s + 10.10 s + 9.26 s = 38.31 seconds.