Question

The height h in feet of an object t seconds after it is dropped can be modeled by the quadratic equation h=-16t^2+h0, where h0 is the initial height of the object. Solve the equation h=-16t^2+255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.

Answer 1

Answer:

The rock will take approximately 3.992 seconds to reach the canyon floor.

Step-by-step explanation:

For all $a\cdot t^{2}+b\cdot t + c = 0$, its roots are determined by the Quadratic Formula:

$t = \frac{-b\pm\sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}$

In this case, it corresponds to instants when rock is either launched or hits the floor. If we know that $a = -16$, $b = 0$ and $c = 255$, the time it takes the rock to reach the canyon floor is:

$t = \frac{-0\pm\sqrt{(0)^{2}-4\cdot (-16)\cdot (255)}}{2\cdot (-16)}$

$t \approx 3.992\,s$

The rock will take approximately 3.992 seconds to reach the canyon floor.