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Answer :
To determine the force exerted on Zach due to elevator's braking, deceleration is calculated as -2.5 m/s^2 and the force is found using Newton's second law, resulting in a force of 210 N directed upwards.
To find the force exerted on Zach due to the elevator's braking, we need to calculate the deceleration and then use Newton's second law of motion.
Firstly, we can find the deceleration using the formula a = Δv / t, where Δv is the change in velocity and t is the time it takes for the change.
Since the elevator comes to a stop, the final velocity will be 0 m/s and the initial velocity is given as 8 m/s.
The time taken to stop is given as 3.2 s, therefore, a = (0 - 8) m/s / 3.2 s = -2.5 m/s2. The negative sign indicates deceleration.
According to Newton's second law, F = ma, where F is the force, m is the mass, and a is the acceleration (or in this case deceleration). Zach's mass is given as 84 kg.
Therefore, the force exerted on Zach can be calculated as F = 84 kg * (-2.5 m/s2) = -210 N.
The negative sign indicates that the force exerted on Zach is in the opposite direction of the initial motion, which is upwards while the elevator is decelerating downwards.
If we are looking for the magnitude of the force, we would say that it is 210 N.
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