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?

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?
The stick hits the ground at about

GPT 3.5 · Answer

To find the time at which the stick hits the ground, we need to find the value of t when h = 0.

Therefore, we need to solve the equation -16t^2 + 85 = 0.

Simplifying this equation, we have:
-16t^2 = -85.

Dividing both sides by -16, we get:
t^2 = 85/16.

Taking the square root of both sides, we have:
t = ±√(85/16).

Since time cannot be negative in this context, we take the positive square root.

Therefore, the stick hits the ground at about t = √(85/16) seconds.