An elevator in a hotel moves at 20 feet per second. leaving from the ground floor, its height in feet after t seconds is given by the formula h(t)=20t. A bolt comes loose in the elevator shaft above, and its height in feet after falling for t seconds is given by h(t)=-16t^2+200. At what time and at what height does the bolt hit the elevator?

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kdrdixon kdrdixon · Answer 1 · 2019-05-12T23:45:43+02:00

Answer:

After 7.5 seconds and a height of 0

Step-by-step explanation:

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raphealnwobi raphealnwobi · Answer 2 · 2021-11-04T12:06:10+01:00

The time taken for the bolt to hit the elevator is 3 seconds, at a height of 60 feet.

Given that the elevator height is h(t)=20t while the bolt height is given by h(t)=-16t² + 200.

At the point when the bolt hit the elevator, they would be at the same height, hence:

-16t² + 200 = 20t

16t² + 20t - 200 = 0

t = -4.2 or t = 3

Therefore the time taken for the bolt to hit the elevator is 3 seconds, the height is:

h(3) = 20(3) = 60 feet

The time taken for the bolt to hit the elevator is 3 seconds, at a height of 60 feet.

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