Question

You are an engineer in charge of designing a new generation of elevators for a prospective upgrade to the Empire State Building. Before the state legislature votes on funding for the project, they would like you to prepare a report on the benefits of upgrading the elevators. One of the numbers that they have requested is the time it will take the elevator to go from the ground floor to the 102nd floor observatory. They are unlikely to approve the project unless the new elevators make the trip much faster than the old elevators.

If state law mandates that elevators cannot accelerate more than 3.30 m/s2 or travel faster than 10.3 m/s , what is the minimum time in which an elevator can travel the 373 m from the ground floor to the observatory floor?

Answer 1

39.3 s

Step-by-step explanation:

During acceleration:

v₀ = 0 m/s

v = 10.3 m/s

a = 3.30 m/s²

Find t and Δy.

v = at + v₀

10.3 = (3.30)t + 0

t = 3.12

v² = v₀² + 2aΔy

(10.3)² = 0² + 2(3.30)Δy

Δy = 16.1

Deceleration is at the same rate, so it also takes 3.12 seconds and 16.1 meters.

The remaining distance is:

373 m − 2(16.1 m) = 340.8 m

The time required at the maximum speed is:

t = 340.8 m / 10.3 m/s

t = 33.1 s

The total time is:

33.1 s + 2(3.12 s) = 39.3 s