Question

The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation h = -16t2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.

Answer 1

H=-16t^2+255
-255=-16t^2
15.9375=t^2
3.99=t

Answer 2

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.