Final answer:
The magnitude of the girl's displacement after swimming directly across and being drifted downstream by a stream 15 meters wide is calculated using the Pythagorean theorem, and it is approximately 21.2 meters.
Step-by-step explanation:
The question revolves around calculating the magnitude of displacement for a girl who attempts to swim directly across a stream but also drifts downstream. To find the displacement, we use the Pythagorean theorem which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, the girl swims 15 meters across and drifts 15 meters downstream, forming a right-angled triangle.
Therefore, the magnitude of her displacement is the hypotenuse of this triangle and can be calculated as follows:
Displacement = √(15² + 15²) = √(225 + 225) = √450 ≈ 21.2 meters.
Thus, the magnitude of the girl's displacement is closest to 21.2 meters.