an object is thrown off a 256 - foot - tall building, and the distance of the object from the ground is…

an object is thrown off a 256 - foot - tall building, and the distance of the object from the ground is measured every second. the function that models the height, h, of the object after t seconds is h(t)=-16t^{2}+96t + 256. determine the time when the object hits the ground. after how many seconds does the object hit the ground? 2 4 8 16

an object is thrown off a 256 - foot - tall building, and the distance of the object from the ground is measured every second. the function that models the height, h, of the object after t seconds is h(t)=-16t^{2}+96t + 256. determine the time when the object hits the ground. after how many seconds does the object hit the ground? 2 4 8 16

Answer

Explanation:

Step1: Set height to 0

When the object hits the ground, $h(t)=0$. So we set $-16t^{2}+96t + 256=0$.

Step2: Divide by -16

Divide the entire equation by -16 to simplify: $t^{2}-6t - 16=0$.

Step3: Factor the quadratic

Factor the quadratic equation: $(t - 8)(t+ 2)=0$.

Step4: Solve for t

Set each factor equal to zero: $t - 8=0$ gives $t = 8$; $t+2=0$ gives $t=-2$. Since time cannot be negative in this context, we discard $t=-2$.

Answer:

C. 8