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
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.