Final answer:
To find the rate of change of the distance between the car and the person at a certain instant, we need to consider the position of the car and the person as functions of time. The rate of change of the distance between the car and the person at that instant is -1 meter per second. option a is correct
Step-by-step explanation:
option a is correct To find the rate of change of the distance between the car and the person at a certain instant, we need to consider the position of the car and the person as functions of time. Let's assume that the person's position is given by P(t) and the car's position is given by C(t), where t is the time in seconds.
The person is standing 15 meters east of the intersection, so the person's position function is P(t) = 15. The car is driving towards the intersection from the north at a rate of 1 meter per second, so the car's position function is C(t) = -t.
The distance between the car and the person at a certain instant is given by the absolute value of the difference between their positions: |C(t) - P(t)| = |-t - 15|. At the instant when the car is 8 meters from the intersection, we have |-t - 15| = 8. Solving this equation, we get t = -23.
The rate of change of the distance between the car and the person at that instant is the derivative of the distance function with respect to time. Taking the derivative of the distance function, we get: d/dt(|-t - 15|) = -1. Since t = -23, the rate of change of the distance between the car and the person at that instant is -1 meter per second. Therefore, the correct answer is Choice A. -√65.