Question

(9 points)
a cannon ball is launched upward with a velocity of 128 feet per second from the top of a 144 - foot tall building. its height after t seconds is given by the equation $s=-16t^{2}+128t + 144$. when does the cannon ball hit the ground?
the cannon ball hits the ground after
submit answers show me another
you have attempted this problem 0 times. you have 3 attempts left before new version will be requested.
you have unlimited attempts remaining.
email instructor

Explanation:

Step1: Set height equal to 0

When the cannon - ball hits the ground, $S = 0$. So we set up the equation $-16t^{2}+128t + 144=0$. Divide the entire equation by -16 to simplify: $t^{2}-8t - 9 = 0$.

Step2: Factor the quadratic equation

We factor the quadratic equation $t^{2}-8t - 9=(t - 9)(t+1)=0$.

Step3: Solve for t

Using the zero - product property, if $(t - 9)(t + 1)=0$, then $t-9 = 0$ or $t + 1=0$. Solving $t-9 = 0$ gives $t = 9$, and solving $t + 1=0$ gives $t=-1$. Since time $t$ cannot be negative in this context, we discard $t=-1$.

Answer:

9