Final answer:
The scale reading for a 60.0 kg person in a decelerating downward elevator is closest to 469 N, as it takes into account both the person's weight and the upward deceleration of the elevator.
Step-by-step explanation:
The student is asking about the apparent weight of a person in an elevator that is decelerating while moving downward. To solve the mathematical problem completely, we need to calculate the net force acting on the person using Newton's second law. Since the elevator is decelerating, the scale reading will be less than the actual weight of the person.
The actual weight (W) of the person is given by:
W = mg = (60.0 kg)(9.80 m/s²) = 588 N
The elevator is decelerating upwards (slowing down while moving downward) which means there is an upward acceleration, so the net force (Fnet) on the person is:
Fnet = ma
Here, 'a' is the acceleration of the elevator, and 'm' is the mass of the person. To find the scale reading (Fs), we must subtract the force due to the elevator's deceleration from the person's weight:
Fs = W - ma
Fs = (60.0 kg)(9.80 m/s²) - (60.0 kg)(2.00 m/s²)
Fs = 588 N - 120 N = 468 N.
Therefore, the reading on the scale is closest to 469 N, which corresponds to option C).
We mention correct option answer in the final answer: The scale reading is closest to 469 N (Option C).