an cannon ball is shot upward at a rate of 180 feet per second from ground level. the cannon ball follows…
an cannon ball is shot upward at a rate of 180 feet per second from ground level. the cannon ball follows the path of the function h(t)=-16t² + 180t. determine when the cannon ball hits the ground. answer: the cannon ball will hit the ground after select an answer note: round any numerical responses to two decimal places. if there are multiple them with commas. feet seconds feet per second none of these units question help: message instructor submit question jump to answer
Answer
Explanation:
Step1: Set height function to 0
When the cannon - ball hits the ground, $h(t)=0$. So we set $-16t^{2}+180t = 0$.
Step2: Factor out t
Factor out $t$ from the left - hand side of the equation: $t(-16t + 180)=0$.
Step3: Solve for t
Using the zero - product property, if $ab = 0$, then either $a = 0$ or $b = 0$. For $t=0$, this represents the initial time when the cannon - ball is fired. For $-16t+180 = 0$, we solve for $t$: First, add $16t$ to both sides: $180=16t$. Then, divide both sides by 16: $t=\frac{180}{16}=\frac{45}{4}=11.25$.
Answer:
11.25 seconds