Question

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

Explanation:

Step1: Set the height function equal to zero

When the object hits the ground, \(h(t) = 0\). So we have the equation \(-16t^{2}+96t + 256=0\). Divide the entire equation by \(-16\) to simplify: \(t^{2}-6t - 16=0\).

Step2: Factor the quadratic equation

We need to find two numbers that multiply to \(-16\) and add up to \(-6\). The numbers are \(-8\) and \(2\). So the factored form is \((t - 8)(t+ 2)=0\).

Step3: Solve for \(t\)

Set each factor equal to zero:

• \(t - 8=0\) gives \(t = 8\).
• \(t+2=0\) gives \(t=-2\). But time \(t\) cannot be negative in this context.

Answer:

\(8\) (corresponding to the option \(8\))