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 29 laps in a swimming pool that is 23 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.
If instead, the swimmer makes 29.5 laps in the same pool in 2.5 h, determine the total distance the swimmer traveled, the swimmer's total displacement, the swimmer's average velocity, and the swimmer's average speed.
Part A
Distance = 29•(2•23) = 1334 m
Displacement =0 (he started and finished at the same point)
Average velocity= displacement/time = 0
Average speed = distance/time = 1334/2.5•3600=0.148 m/s
Part B
Distance 29.5•(2•23)= 1357 m.
Displacement =23 m
Average velocity= displacement/time =23/2.5•3600 =0.00256 m/s
Average speed = distance/time = 1357/2.5•3600=0.1508 m/s
To determine the distance the swimmer traveled, we need to calculate the total distance covered in 29 laps.
Distance = Number of laps * Length of the pool
Distance = 29 laps * 2 (since each lap is from one end to the other and back) * 23 m (length of the pool)
Distance = 29 * 2 * 23 m
Distance = 1334 m
So, the swimmer traveled a distance of 1334 meters.
To determine the total displacement of the swimmer, we need to find the difference between the initial and final positions. Since the swimmer ends up at the same position as the starting point after completing 29 laps, the total displacement is 0 meters.
The swimmer's average velocity can be calculated using the formula:
Average Velocity = Total Displacement / Time
Since the total displacement is 0, the average velocity is also 0.
The swimmer's average speed can be calculated using the formula:
Average Speed = Total Distance / Time
Average Speed = 1334 m / 2.5 h
Average Speed = 533.6 m/h
So, the swimmer's average speed is approximately 533.6 meters per hour.
For the case when the swimmer makes 29.5 laps in the same pool in 2.5 h, the calculations are as follows:
Total Distance = Number of laps * Length of the pool
Total Distance = 29.5 laps * 2 * 23 m
Total Distance = 1357 m
Total Displacement = 0 (since the swimmer ends up at the same position)
Average Velocity = Total Displacement / Time
Average Velocity = 0 / 2.5 h
Average Velocity = 0 m/h
Average Speed = Total Distance / Time
Average Speed = 1357 m / 2.5 h
Average Speed = 542.8 m/h
So, the swimmer's total distance traveled is 1357 meters, the total displacement is 0 meters, the average velocity is 0 m/h, and the average speed is 542.8 meters per hour.
To determine the distance the swimmer traveled, you need to multiply the number of laps by the length of the pool. In the first case, where the swimmer made 29 laps:
Distance = Number of laps * Pool length
Distance = 29 laps * 23 m
Distance = 667 m
Therefore, in the first case, the swimmer traveled a distance of 667 meters.
To calculate the total displacement of the swimmer, you need to find the difference between the initial position and the final position. Since the swimmer completes the laps back and forth, the total displacement is zero.
Total Displacement = Final position - Initial position
Total Displacement = 0 - 0
Total Displacement = 0
In the first case, the swimmer's total displacement is zero.
To calculate the swimmer's average velocity, you need to divide the total displacement by the total time taken.
Average Velocity = Total Displacement / Total Time taken
Average Velocity = 0 / 2.5 h
Average Velocity = 0 m/h
In the first case, the swimmer's average velocity is 0 meters per hour.
To calculate the swimmer's average speed, you need to divide the total distance traveled by the total time taken.
Average Speed = Total Distance / Total Time taken
Average Speed = 667 m / 2.5 h
Average Speed = 266.8 m/h
In the first case, the swimmer's average speed is approximately 266.8 meters per hour.
Now let's move on to the second case, where the swimmer makes 29.5 laps:
To determine the total distance the swimmer traveled, we would first calculate the distance traveled for the 29 laps, and then add the distance for the extra half lap.
Distance = Number of laps * Pool length
Distance = 29 laps * 23 m
Distance = 667 m
For the extra half lap:
Distance = 0.5 * Pool length
Distance = 0.5 * 23 m
Distance = 11.5 m
Total Distance = Distance for 29 laps + Distance for extra half lap
Total Distance = 667 m + 11.5 m
Total Distance = 678.5 m
Therefore, in the second case, the swimmer traveled a total distance of 678.5 meters.
Since the swimmer completes the laps back and forth, the total displacement is still zero.
Total Displacement = 0
The calculations for average velocity and average speed would be the same as in the first case, because the total displacement and the total time taken remain unchanged.
Average Velocity = 0 m/h
Average Speed = 266.8 m/h
In the second case, the swimmer's average velocity is still 0 meters per hour, and the swimmer's average speed is still approximately 266.8 meters per hour.