Answer:
The rock will reach to the canyon floor in 3.99 seconds.
Step-by-step explanation:
The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation
\(h=-16t^2+255\)
Where, h0 is the initial height of the object.
It can be written as
\(h=-16t^2+0t+255\)
The height of the object is zero if it will reach to the canyon floor.
\(0=-16t^2+0t+255\)
Quadratic formula:
\(t=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)
Here a=-16, b=0 and c=255.
\(t=\frac{-0\pm \sqrt{0^2-4(-16)(255)}}{2(-16)}\)
\(t=\frac{\pm \sqrt{16320}}{-32}\)
\(t=\pm 3.99\)
Time cannot be negative, therefore the rock will reach to the canyon floor in 3.99 seconds.
