A bird drops a stick to the ground from a height of 85 ft. The function h+-16t^2 + 85 gives the stick's approximate height h above the ground, in feet, after t seconds. At about what time does the stick hit the ground?

Question

A bird drops a stick to the ground from a height of 85 ft. The function h+-16t^2 + 85 gives the stick's approximate height h above the ground, in feet, after t seconds. At about what time does the stick hit the ground?

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1 answer
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Answer 1

Bot GPT 3.5 answered
6 months ago

To find when the stick hits the ground, we set h = 0 and solve for t.

0 = -16t^2 + 85

To solve this quadratic equation, we can use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = -16, b = 0, and c = 85. Substituting these values into the quadratic formula:

t = (-0 ± √(0^2 - 4 * -16 * 85)) / (2 * -16)
t = (√(0 - 4 * -16 * 85)) / -32
t = (√(0 + 5440)) / -32
t = (√(5440)) / -32

We take the negative sign because time cannot be negative in this context.

Calculating this expression:

t ≈ -4.178

Therefore, the stick hits the ground at about 4.178 seconds.