An athlete swims the length of a 46.0 m pool in 21.0 s and makes the return trip to the starting position in 23.0 s. Determine her average velocities in each of the following below. (Take Δx to be positive when the displacement is in the direction she swims during the first half of the trip.)
To determine the athlete's average velocities, we need to calculate the displacement for each leg of the journey and divide it by the time it took.
First, let's calculate the displacement for the first leg of the trip, which is swimming the length of the pool. The displacement is given by the formula:
displacement = final position - initial position
Since the athlete swims the length of the pool, the final position is 46.0 m and the initial position is 0. Therefore:
displacement = 46.0 m - 0 = 46.0 m
Now, let's calculate the average velocity for the first leg of the trip using the formula:
average velocity = displacement / time
average velocity = 46.0 m / 21.0 s ≈ 2.190 m/s
Therefore, the athlete's average velocity for the first leg of the trip is approximately 2.190 m/s.
Next, let's calculate the displacement for the return trip to the starting position. Since the athlete returns to the starting position, the final position is 0 and the initial position is 46.0 m. Therefore:
displacement = 0 - 46.0 m = -46.0 m
Note that the displacement is negative because the athlete is swimming in the opposite direction.
Now, let's calculate the average velocity for the return trip:
average velocity = displacement / time
average velocity = -46.0 m / 23.0 s ≈ -2.000 m/s
Therefore, the athlete's average velocity for the return trip is approximately -2.000 m/s.
In summary, the athlete's average velocity during the first leg of the trip is approximately 2.190 m/s, and the average velocity during the return trip is approximately -2.000 m/s.