Final answer:
The position equation for person A, starting 4,500 m north of person B and moving at 15.0 m/s after a delay of 100 seconds, is x_A(t) = 4500 m + 15.0 m/s × (t - 100 s), considering person B's starting point as the origin.
Step-by-step explanation:
The question is asking for the position equation of person A in reference to person B's starting location on the highway. First, we note that person A starts her trip 4,500 m North of person B and moves at a constant speed of 15.0 m/s. Person B's position is considered as the origin (0 m), and person A starts 100 seconds after person B. We can write the position equation for person A with respect to time as:
x_A(t) = x_{A0} + v_{A} × (t - t_{delay})
Where x_{A0} is the initial position of A relative to B, v_{A} is the velocity of person A, t is the time variable, and t_{delay} is the time delay before person A starts, which is 100 seconds. Substituting the values we get:
x_A(t) = 4500 m + 15.0 m/s × (t - 100 s)
This is the position equation for person A with person B's location as the origin.