Physics: Jack and Jill exercise in a 25.0 m long swimming pool. Jack swims 9 lengths of the pool in 155.5 s (2 min and 35.5 s) , whereas Jill, the faster swimmer, covers 10 lengths in the same time interval. Find the average velocity and average speed of each swimmer.

Not enough for it to get airborne within the next 30 seconds....

Jack and Jill exercise in a 25.0 m long swimming

Ответ:

maskythegamer

17.03.2022

Physics

Jack:

Average velocity: $\vec v_{avg, Ja} = +0.161\,\frac{m}{s}$ , Average speed: $v_{avg,Ja} = 1.447\,\frac{m}{s}$

Jill:

Average velocity: $\vec v_{avg, Ji} = 0\,\frac{m}{s}$ , Average speed: $v_{avg,Ja} = 1.608\,\frac{m}{s}$

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:

$\vec v_{avg} = \frac{1}{\Delta t} \cdot \Sigma_{i=1}^{n} \vec r_{i}$ (1)

Where:

$\Delta t$ - Total time, measured in seconds.

$\vec r_{i}$ - 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:

$v_{avg} = \frac{1}{\Delta t} \cdot \|\vec r_{i}\|$ (2)

Where $\|\vec r_{i}\|$ 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 ( $\Delta t = 155.5\,s$ , $\vec r_{1} = \vec r_{3} = \vec r_{5} = \vec r_{7} = \vec r_{9} = +25\,m$ , $\vec r_{2} = \vec r_{4} = \vec r_{6} = \vec r_{8} = -25\,m$ )

$\vec v_{avg,Ja} = \frac{5\cdot (25\,m)+4\cdot (-25\,m)}{155.5\,s}$

$\vec v_{avg, Ja} = +0.161\,\frac{m}{s}$

Jack - Average speed ( $\Delta t = 155.5\,s$ , $\|\vec r_{i}\| = 25\,m$ , n = 9 )

$v_{avg,Ja} = \frac{9\cdot (25\,m)}{155.5\,s}$

$v_{avg,Ja} = 1.447\,\frac{m}{s}$

Jill - Average velocity ( $\Delta t = 155.5\,s$ , $\vec r_{1} = \vec r_{3} = \vec r_{5} = \vec r_{7} = \vec r_{9} = +25\,m$ , $\vec r_{2} = \vec r_{4} = \vec r_{6} = \vec r_{8} = \vec r_{10} = -25\,m$ )

$\vec v_{avg,Ji} = \frac{5\cdot (25\,m)+5\cdot (-25\,m)}{155.5\,s}$

$\vec v_{avg, Ji} = 0\,\frac{m}{s}$

Jill - Average speed ( $\Delta t = 155.5\,s$ , $\|\vec r_{i}\| = 25\,m$ , n = 10 )

$v_{avg,Ji} = \frac{10\cdot (25\,m)}{155.5\,s}$

$v_{avg,Ja} = 1.608\,\frac{m}{s}$

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Jack and Jill exercise in a 25.0 m long swimming pool. Jack swims 9 lengths of the pool in 155.5 s (2 min and 35.5 s) , whereas Jill, the faster swimmer, covers 10 lengths in the same time interval. Find the average velocity and average speed of each swimmer.

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