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 + h_0 ), where ( h_0 ) is the initial height of the object. suppose a small rock dislodges from a ledge that is 256 ft above a canyon floor. solve the equation ( h = -16t^2 + 256 ) for ( t ) using the quadratic formula to determine the time it takes the rock to reach the canyon floor (\bigcirc t approx 0.87 s \bigcirc t approx 4 s \bigcirc t = 8.5 s \bigcirc t = 16 s)

Explanation:

Step1: Set height to 0 (canyon floor)

$0 = -16t^2 + 255$

Step2: Rearrange the equation

$16t^2 = 255$

Step3: Isolate $t^2$

$t^2 = \frac{255}{16}$

Step4: Solve for positive $t$

$t = \sqrt{\frac{255}{16}} = \frac{\sqrt{255}}{4} \approx 4.0$

Answer:

$t=4\ \text{s}$