✔ 最佳答案
Energy required to life the elevator and 3 people equals to the potential energy at 641 ft.
Potential energy = mgh = (459 + 253) kg x 9.81 ms^-2 x (641 x 0.3048) m = 1364652 J
When the elevator start drop, the velocity V at top is 0 ms^-1.
When the elevator drop to 200 ft,
gain of kinetic energy = lost of potential energy
1/2 m v^2 = mgh
1/2 v^2 = gh
1/2 v^2 = 9.81 x (641 - 200) x 0.3048
v^2 = 2637.26
v = 51.35 ms^-1
Total energy at ground equals total potential energy at top. Then, the final velocity at ground,
1/2 mv^2 = 1364652 J
v^2 = 1364652 x 2 / (459+253)
v = 61.91 ms^-1
The time T for the elevator and 2 people accelerate from 0 ms^-1 to 61.91 ms^-1 under gravity,
9.81 ms^-2 x T = 61.91 ms^-1
T = 6.31 s