Question

1. -/8 points if you have swam one lap in a swimming pool, that means you have swam from one end to the other and back. in 2.5 h, a swimmer makes exactly 94 laps in a swimming pool that is 21 m long. determine the distance the swimmer traveled, the total displacement of the swimmer, the swimmers average velocity, and the swimmers average speed. distance km b.) displacement km c.) average velocity km/h d.) average speed if instead, the swimmer makes 94.5 laps in the same pool in 2.5 h determine the total

Explanation:

Step1: Calculate the distance

The length of one lap is \(l = 21\space m\). The number of laps \(n=94\).
The distance \(d\) is given by \(d=n\times2l\) (since one lap is to - and - fro).

$$d = 94\times2\times21\space m$$

$$d=94\times42\space m$$

$$d = 3948\space m$$

Convert meters to kilometers: \(d=\frac{3948}{1000}\space km=3.948\space km\)

Step2: Calculate the displacement

Since the swimmer starts and ends at the same point after completing an integer number of laps (a full to - and - fro motion), the displacement \(\Delta x = 0\space km\)

Step3: Calculate the average velocity

The formula for average velocity \(v_{avg}=\frac{\Delta x}{t}\).
Given \(t = 2.5\space h\) and \(\Delta x=0\space km\)

$$v_{avg}=\frac{0}{2.5}\space km/h = 0\space km/h$$

Step4: Calculate the average speed

The formula for average speed \(s_{avg}=\frac{d}{t}\)
Given \(d = 3.948\space km\) and \(t = 2.5\space h\)

$$s_{avg}=\frac{3.948}{2.5}\space km/h$$

$$s_{avg}=1.5792\space km/h\approx1.58\space km/h$$

Answer:

b.) Displacement: \(0\space km\)
c.) Average velocity: \(0\space km/h\)
d.) Average speed: \(1.58\space km/h\)