Question

A piece of rope falls out of a hot air

Answer 1

Answer: 18 seconds

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Explanation:

The equation should be h(t) = -16t^2 + (initial height). If you subtract off the initial height, then you'll have a negative starting height, which is not correct. Try plugging t = 0 into h(t) = -16t^2 - (initial height) and you'll see what I mean.

The initial height is 5184. We want to find the t value when h(t) = 0. So we want to find the time value when the height is 0.

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h(t) = -16t^2 + (initial height)

h(t) = -16t^2 + 5184

0 = -16t^2 + 5184

16t^2 = 5184

t^2 = 5184/16

t^2 = 324

t = sqrt(324)

t = 18

It takes 18 seconds for the rope to hit the ground.