Question

suppose that a movie is being filmed an action shot requires an object to be thrown upward with an initial velocity of 64 feet per second off the top of the plaza, a height of 720 feet the height h(t) in feet of the object after t seconds is given by the function h(t)= - 16t² + 64t + 720 determine how long before the object strikes the ground (hint let the height, h(t), be 0 and solve for t ) the object will strike the ground in □ (type a whole number )

Explanation:

Step1: Set up the equation

Set \(h(t) = 0\), so \(-16t^{2}+64t + 720=0\). Divide the entire equation by \(-16\) to simplify: \(t^{2}-4t - 45=0\).

Step2: Factor the quadratic equation

We need to find two numbers that multiply to \(-45\) and add up to \(-4\). The numbers are \(-9\) and \(5\). So, \((t - 9)(t+ 5)=0\).

Step3: Solve for \(t\)

Using the zero - product property \(t - 9=0\) or \(t + 5=0\). Solving \(t - 9=0\) gives \(t=9\), and solving \(t + 5=0\) gives \(t=-5\). Since time \(t\geq0\), we discard \(t=-5\).

Answer:

The object will strike the ground in \(9\) seconds.