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 1.50 m/s2 or travel faster than 12.8 m/s , what is the minimum time in which an elevator can travel the 373 m from the ground floor to the observatory floor?

minimum travel time: s

Answer 1

Only method is accelerate the elevator from rest to 12.8 m/s(Max Velocity Under State Law) by the rate of 1.5 m/s² (Max Acceleration Under State Law) ,then travel the rest with constant velocity of 12.8 m/s and finally coming to rest

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First find time taken to accelerate

Use Formula

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Now distance Covered in that Time

Use Formula

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While stopping the elevator needs same time to decelerate and stop

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Now distance Covered in that Time t₃

Use Formula

Remaining Height will be covered under constant Velocity of 12.8 m/s

Remaining Height ,

Speed =Distance /Time

Time =Distance/Speed

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Total Time

ANSWER:

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