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 h, a swimmer makes exactly 58 laps in a swimming pool that is 47 m long. Determine the distance the swimmer traveled, the total displacement of the swimmer, the swimmer's average velocity, and the swimmer's average speed.
a.) Distance in km
b.) Displacement in km
c.) Average velocity in km/h
d.) Average speed in km/h
If instead, the swimmer makes 58.5 laps in the same pool in 2 h, determine the total distance the swimmer traveled, the swimmer's total displacement, the swimmer's average velocity, and the swimmer's average speed.
e.) Distance in km
f.) Displacement in km
g.) Average velocity in km/h
h.) Average speed in km/h
a. d = 58Laps * (2*47)m/Lap = Distance in m. Divide by 1000 to change to
km.
b. D = straight line distance from starting point to the end = 0 km.
c. V = D/t = 0/2 = 0.
d. Speed = d/t
e. 58.5Laps * (2*47)m/Lap = distance in m. Change to km.
f. D = 0.5Laps * (2*47)m/Lap = Disp. in m. Change to km.
g. V = D/t.
h. Speed = d/t.
To solve these problems, we need to first calculate the total distance and displacement for each scenario, and then use those values to find the average velocity and speed. Let's start by calculating the distance traveled.
a.) To find the distance in kilometers, we need to convert the length of the pool and the number of laps into kilometers. Given that the pool length is 47 m and the swimmer makes 58 laps, the total distance traveled is:
Distance = (Pool Length) x (Number of Laps)
= 47 m x 58
= 2726 m
To convert this to kilometers, we divide by 1000 since there are 1000 meters in 1 kilometer:
Distance in km = 2726 m / 1000
= 2.726 km
Therefore, the swimmer traveled a distance of 2.726 km.
b.) Displacement is the shortest distance between the starting point and the finishing point. In this case, since the swimmer swims back and forth between the two ends, the displacement is zero. So, the displacement is 0 km.
c.) Average velocity is the total displacement divided by the total time. In this case, the displacement is zero, and the total time is given as 2 hours. Therefore, the average velocity is zero km/h.
d.) Average speed is the total distance divided by the total time. In this case, the total distance traveled is 2.726 km, and the total time is 2 hours:
Average speed = Total Distance / Total Time
= 2.726 km / 2 h
= 1.363 km/h
Therefore, the swimmer's average speed is 1.363 km/h.
Now let's move on to the second scenario.
e.) Similar to the previous scenario, the swimmer makes 58.5 laps in a 47 m pool. The total distance traveled is:
Distance = (Pool Length) x (Number of Laps)
= 47 m x 58.5
= 2749.5 m
Converting this to kilometers:
Distance in km = 2749.5 m / 1000
= 2.7495 km
Therefore, the swimmer traveled a total distance of 2.7495 km.
f.) Displacement remains zero, as the swimmer swims back and forth between the two ends.
g.) Average velocity is again calculated by dividing the total displacement by the total time. Since the displacement is zero, the average velocity remains zero km/h.
h.) Average speed is calculated by dividing the total distance by the total time. In this case, the total distance traveled is 2.7495 km and the total time is 2 hours:
Average speed = Total Distance / Total Time
= 2.7495 km / 2 h
= 1.37475 km/h
Therefore, the swimmer's average speed is 1.37475 km/h.