The Shanghai Tower Is The Tallest In China. But The Chinese Are Flocking To It For Another Reason

Calculus Level 3

The Shanghai Tower is the second tallest in the world, and has an architectural height of 632 meters. It is equipped with the world’s fastest elevator, which can travel at 18 m/s. Several newspapers reported that it will reach the top in just under 36 seconds, which isn't true due to physical limitations.

Firstly, the top floor of the building is only 557 meters high. Secondly, in order to prevent accidents to pregnant women, the maximum allowed acceleration is 1.25 m/s\(^2\). Thirdly, for passenger comfort, the maximum jerk (rate of change of acceleration) is 2.50 m/s\(^3 \).

Based on these measurements, what is the shortest time that it would take an elevator to reach the top floor?

Details and assumptions

It actually takes the elevator 55 seconds to ascend 565 meters, due to further physical limitations. You can read more in the Mitsubishi Elevator Technical Paper.


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