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 336 feet. the height h(t) in feet of the object after t seconds is given by the function h(t) = - 16t² + 64t + 336. 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 \(-16t^{2}+64t + 336=0\). Divide the entire equation by \(-16\) to simplify: \(t^{2}-4t - 21=0\).

Step2: Factor the quadratic equation

Factor \(t^{2}-4t - 21\). We need two numbers that multiply to \(-21\) and add up to \(-4\). These numbers are \(-7\) and \(3\). So, \((t - 7)(t+ 3)=0\).

Step3: Solve for \(t\)

Set each factor equal to zero:

• \(t - 7=0\) gives \(t = 7\).
• \(t + 3=0\) gives \(t=-3\).

Since time \(t\) cannot be negative in this context (we are talking about time after the object is thrown), we discard \(t=-3\).

Answer:

The object will strike the ground in \(7\) seconds.