Question

A bird drops a stick to the ground from a height of 85 ft. The function ℎ = −162+85h = −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?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the time when the stick hits the ground, we need to solve the equation h = 0.

-162 + 85t = -16t^2 + 85

Rearranging the equation, we get:
-16t^2 + 85t - 247 = 0

We can solve this quadratic equation by factoring or by using the quadratic formula. Using the quadratic formula:
t = (-b ± sqrt(b^2 - 4ac)) / 2a

a = -16, b = 85, c = -247

t = (-85 ± sqrt(85^2 - 4(-16)(-247))) / 2(-16)
t = (-85 ± sqrt(7225 - 19712)) / -32
t = (-85 ± sqrt(-12487)) / -32

Since the value inside the square root is negative, there are no real solutions to this equation. Therefore, the stick does not hit the ground according to this model.

However, it is more likely that there is an error in the given function, as it does not make sense for the stick to never hit the ground.