Final answer:
Using Newton's second law and the constant acceleration formula, the force exerted on Zach during the elevator's braking is calculated as -206.474 N. However, this answer does not match any of the provided options, indicating a potential mistake in the options given.
Step-by-step explanation:
To determine the force exerted on Zach during the braking process of the elevator, we must calculate the acceleration of the elevator during braking and then use Newton's second law to find the force exerted on Zach.
First, we'll find the acceleration using the following formula for constant acceleration:
a = (v_f - v_i) / t
where:
v_f = final velocity (0 m/s, since the elevator comes to a stop),
v_i = initial velocity (9 m/s, descending),
t = time taken to stop (3.4 s).
Plugging these values in, we get:
a = (0 m/s - 9 m/s) / 3.4 s = -9 m/s / 3.4 s = -2.6471 m/s²
We use a negative sign because the elevator is decelerating (slowing down). Now we'll use Newton's second law, F = m * a, where m is Zach's mass (78 kg).
F = 78 kg * (-2.6471 m/s²) = -206.474 N
The negative sign indicates the force is directed upwards, which opposes the downward motion of the elevator. However, in terms of magnitude, the force is 206.474 N. Since this isn't any of the options, it seems there's been a mistake. The closest option in terms of magnitude is option 3) 702 N, which suggests the options may not be accurately reflecting the correct calculations. Therefore, none of the provided options is correct.