If you have swam one lap in a swimming pool, that means you have swam from one end to the other and back. In 4.5 h, a swimmer makes exactly 69 laps in a swimming pool that is 35 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.
DISTANCE
D = 2 * (# of laps) * (length of pool)
D = 2*69*35 = 4830 m
TOTAL DISPLACEMENT
You're going by the swimmer's final position, so if he ends up at the same place he started, the net distance (or in other words, the displacement) is 0.
AVERAGE VELOCITY
Displacement's 0, so average velocity must also be 0 (since avg. velocity = displacement/time).
AVERAGE SPEED
Speed = (total distance)/(time)
Speed = (4830)/(4.5 hours)
Speed = (4830)/(16200 s)
Speed = 0.298 m/s
To determine the distance the swimmer traveled, we can multiply the number of laps by the length of the pool.
Distance = Number of laps × Length of the pool
In this case, the number of laps is 69 and the length of the pool is 35 meters.
Distance = 69 laps × 35 m = 2415 meters
The swimmer traveled a total distance of 2415 meters.
To calculate the total displacement of the swimmer, we need to consider that each lap has two parts - swimming from one end to the other (35 m) and swimming back from the other end to the starting point (35 m). Hence, the displacement for each lap is 0 (since the swimmer returns to the starting point).
Total Displacement = Number of laps × Displacement per lap
In this case, the number of laps is 69 and the displacement per lap is 0.
Total Displacement = 69 laps × 0 = 0 meters
The swimmer's total displacement is 0 meters, as they end up at the same point they started.
To find the swimmer's average velocity, we use the formula:
Average Velocity = Total Displacement ÷ Total Time
Since the total displacement is 0 meters, the average velocity will also be 0.
Average Velocity = 0 meters ÷ 4.5 hours = 0 m/h
The swimmer's average velocity is 0 m/h, as there is no displacement over time.
Lastly, to calculate the swimmer's average speed, we divide the total distance by the total time:
Average Speed = Total Distance ÷ Total Time
In this case, the total distance is 2415 meters and the total time is 4.5 hours.
Average Speed = 2415 meters ÷ 4.5 hours = 537 m/h
The swimmer's average speed is 537 m/h.