First, let's understand the difference between speed and velocity. Speed is a scalar quantity that refers to "how fast an object is moving." It does not contain any information about the direction of the object's movement. On the other hand, velocity is a vector quantity that refers to "the rate at which an object changes its position." It is speed in a given direction.
Now, we can find the total distance each swimmer travels and the average velocity and speed for each.
The total distance Jack swims is 9 lengths * 25.0 m/length = 225.0 m.
His average speed, which is the total distance divided by the time, is 225.0 m / 150.3 s = 1.497 m/s (rounded to three decimal places).
For the average velocity, we need to remember that when Jack finishes swimming, he is back where he started after an odd number of lengths. This means his displacement is one length of the pool or 25.0 m. So his average velocity is 25.0 m / 150.3 s = 0.166 m/s (rounded to three decimal places).
Now for Jill:
The total distance Jill swims is 10 lengths * 25.0 m/length = 250.0 m.
Her average speed is 250.0 m / 150.3 s = 1.663 m/s (rounded to three decimal places).
However, Jill finishes at the opposite end of the pool because she swam an even number of lengths, so her displacement is two lengths or 50.0 m. Therefore, her average velocity is 50.0 m / 150.3 s = 0.333 m/s (rounded to three decimal places).
So:
- Jack's average velocity: 0.166 m/s
- Jack's average speed: 1.497 m/s
- Jill's average velocity: 0.333 m/s
- Jill's average speed: 1.663 m/s