Answer:
Jack:
Average velocity:
, Average speed: ![v_{avg,Ja} = 1.447\,\frac{m}{s}](https://tex.z-dn.net/?f=v_%7Bavg%2CJa%7D%20%3D%201.447%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
Jill:
Average velocity:
, Average speed: ![v_{avg,Ja} = 1.608\,\frac{m}{s}](https://tex.z-dn.net/?f=v_%7Bavg%2CJa%7D%20%3D%201.608%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
Explanation:
We assume that each swimmer returns to the point of the departure each two lengths of the pool.
The average velocity is defined by the following definition:
(1)
Where:
- Total time, measured in seconds.
- i-th Relative vector position, measured in meters.
- Number of lengths done by the swimmer.
And the average speed is represented by the following formula:
(2)
Where
is the norm of the i-th relative vector position, measured in meters.
Now, we proceed to calculate both values for both swimmers:
Jack - Average velocity (
,
,
)
![\vec v_{avg,Ja} = \frac{5\cdot (25\,m)+4\cdot (-25\,m)}{155.5\,s}](https://tex.z-dn.net/?f=%5Cvec%20v_%7Bavg%2CJa%7D%20%3D%20%5Cfrac%7B5%5Ccdot%20%2825%5C%2Cm%29%2B4%5Ccdot%20%28-25%5C%2Cm%29%7D%7B155.5%5C%2Cs%7D)
![\vec v_{avg, Ja} = +0.161\,\frac{m}{s}](https://tex.z-dn.net/?f=%5Cvec%20v_%7Bavg%2C%20Ja%7D%20%3D%20%2B0.161%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
Jack - Average speed (
,
,
)
![v_{avg,Ja} = \frac{9\cdot (25\,m)}{155.5\,s}](https://tex.z-dn.net/?f=v_%7Bavg%2CJa%7D%20%3D%20%5Cfrac%7B9%5Ccdot%20%2825%5C%2Cm%29%7D%7B155.5%5C%2Cs%7D)
![v_{avg,Ja} = 1.447\,\frac{m}{s}](https://tex.z-dn.net/?f=v_%7Bavg%2CJa%7D%20%3D%201.447%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
Jill - Average velocity (
,
,
)
![\vec v_{avg,Ji} = \frac{5\cdot (25\,m)+5\cdot (-25\,m)}{155.5\,s}](https://tex.z-dn.net/?f=%5Cvec%20v_%7Bavg%2CJi%7D%20%3D%20%5Cfrac%7B5%5Ccdot%20%2825%5C%2Cm%29%2B5%5Ccdot%20%28-25%5C%2Cm%29%7D%7B155.5%5C%2Cs%7D)
![\vec v_{avg, Ji} = 0\,\frac{m}{s}](https://tex.z-dn.net/?f=%5Cvec%20v_%7Bavg%2C%20Ji%7D%20%3D%200%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)
Jill - Average speed (
,
,
)
![v_{avg,Ji} = \frac{10\cdot (25\,m)}{155.5\,s}](https://tex.z-dn.net/?f=v_%7Bavg%2CJi%7D%20%3D%20%5Cfrac%7B10%5Ccdot%20%2825%5C%2Cm%29%7D%7B155.5%5C%2Cs%7D)
![v_{avg,Ja} = 1.608\,\frac{m}{s}](https://tex.z-dn.net/?f=v_%7Bavg%2CJa%7D%20%3D%201.608%5C%2C%5Cfrac%7Bm%7D%7Bs%7D)