Jack and Jill exercise in a 25.0-m-long swimming pool. Jack swims nine lengths of the pool in 160.1 seconds (2 minutes and 40.1 seconds), while Jill, the faster swimmer, covers ten lengths in the same time interval. Find the average velocity and average speed of each swimmer.

Well, Jack and Jill sure sound like they're having a splashin' good time! Let's dive into these calculations.

To find the average velocity of a swimmer, we need to divide the total displacement by the total time taken. Since both Jack and Jill are swimming back and forth in the same pool, their displacements are equal to the length of the pool (25.0 m).

So, for Jack, his total displacement is 9 lengths * 25.0 m/length = 225.0 m.
His average velocity is then 225.0 m / 160.1 s ≈ 1.404 m/s.

Meanwhile, for Jill, her total displacement is 10 lengths * 25.0 m/length = 250.0 m.
Her average velocity is 250.0 m / 160.1 s ≈ 1.561 m/s.

Now, to calculate average speed, we just need to divide the total distance traveled by the total time taken. Since distance traveled is just the total number of lengths multiplied by the length of the pool, we can easily find it.

For Jack, his total distance is 9 lengths * 25.0 m/length = 225.0 m.
His average speed is then 225.0 m / 160.1 s ≈ 1.404 m/s. Hey, that's the same as his average velocity! Looks like Jack keeps a consistent pace.

For Jill, her total distance is 10 lengths * 25.0 m/length = 250.0 m.
Her average speed is 250.0 m / 160.1 s ≈ 1.561 m/s. Oh, so Jill went a little faster on average!

So there you have it: Jack's average velocity and average speed are approximately 1.404 m/s, while Jill's average velocity is approximately 1.561 m/s and her average speed is also approximately 1.561 m/s. Happy swimming, you two!

To find the average velocity and average speed of each swimmer, we can use the following formulas:

Average Velocity = Total Displacement / Total Time
Average Speed = Total Distance / Total Time

Let's calculate the average velocity and average speed for each swimmer.

1. Jack's average velocity:
Total Displacement = Number of lengths * Length of the pool
= 9 * 25.0 m
= 225.0 m

Total Time = 160.1 seconds

Average Velocity = Total Displacement / Total Time
= 225.0 m / 160.1 s
≈ 1.404 m/s

2. Jack's average speed:
Total Distance = Number of lengths * Length of the pool
= 9 * 25.0 m
= 225.0 m

Total Time = 160.1 seconds

Average Speed = Total Distance / Total Time
= 225.0 m / 160.1 s
≈ 1.404 m/s

3. Jill's average velocity:
Total Displacement = Number of lengths * Length of the pool
= 10 * 25.0 m
= 250.0 m

Total Time = 160.1 seconds

Average Velocity = Total Displacement / Total Time
= 250.0 m / 160.1 s
≈ 1.561 m/s

4. Jill's average speed:
Total Distance = Number of lengths * Length of the pool
= 10 * 25.0 m
= 250.0 m

Total Time = 160.1 seconds

Average Speed = Total Distance / Total Time
= 250.0 m / 160.1 s
≈ 1.561 m/s

Therefore, the average velocity of Jack is approximately 1.404 m/s, the average speed of Jack is approximately 1.404 m/s, the average velocity of Jill is approximately 1.561 m/s, and the average speed of Jill is approximately 1.561 m/s.

To find the average velocity of each swimmer, we need to calculate the distance each swimmer has covered and the time it took them.

First, let's calculate the distance Jack and Jill covered:

Distance covered by Jack = 9 lengths * 25.0 m/length = 225.0 m
Distance covered by Jill = 10 lengths * 25.0 m/length = 250.0 m

Next, we need to calculate the time taken by both swimmers:

Time taken by Jack = 160.1 seconds
Time taken by Jill = 160.1 seconds

Now, we can calculate the average velocity of each swimmer:

Average velocity = Distance / Time

Average velocity of Jack = 225.0 m / 160.1 s = 1.404 m/s
Average velocity of Jill = 250.0 m / 160.1 s = 1.562 m/s

To find the average speed of each swimmer, we can use the formula:

Average speed = Total distance / Total time

Total distance covered by both Jack and Jill = 225.0 m + 250.0 m = 475.0 m
Total time taken by both Jack and Jill = 160.1 s

Average speed of both Jack and Jill = 475.0 m / 160.1 s = 2.966 m/s

So, the average velocity of Jack is 1.404 m/s, the average velocity of Jill is 1.562 m/s, and the average speed of both Jack and Jill is 2.966 m/s.

Jack: V = d/t = 9*25m/160.1s. = Ans. in

m/s.

Jill: V = d/t = 10*25m/160.1s = Ans. in
m/s.