Final answer:
Using the given force function, we calculate the impulse and determine the magnitude of the girl's final momentum to be 19.375 kg · m/s, not matching the provided answer choices. This suggests there is an error in the question details or the answer options.
Step-by-step explanation:
To determine the magnitude of the girl's momentum at t = 5 s, we'll need to calculate the change in momentum caused by the net force over that period. The initial momentum of the girl is 85.0 kg · m/s eastwards. The net force applied to the girl has a magnitude that changes over time, defined as f = (8.35 N/s)t, directed due west, opposing her initial momentum. The impulse experienced by the girl due to the force is the integral of the force over the time interval (0 to 5 s). The impulse is equal to the change in momentum (Δp).
Impulse = ∫ F dt = ∫ (8.35t) dt from 0 to 5 s = ½ * 8.35 * 5² = 104.375 N · s. This impulse has been applied in the direction opposite to the girl's initial momentum.
The resulting momentum at t = 5 s is: p_final = p_initial - Impulse = 85.0 kg · m/s - 104.375 kg · m/s = -19.375 kg · m/s (due west). Since the question asks for the magnitude, we simply take the absolute value: |p_final| = 19.375 kg · m/s, which is not an answer choice provided. Hence, there seems to be an error either in the question details or the answer options.