check the picture below. That's pretty much a rough graph of an initial speed scenario.
so, we know the ball will hit the ground when h = 0, and we know that r = 48, thus
[tex] \bf h=48t-16t^2\implies \stackrel{h}{0}=48t-16t^2\implies 0=16t(3-t^2)\\\\
-------------------------------\\\\
0=16t\implies 0=t\impliedby \textit{is 0 when it was on the ground at first}\\\\
-------------------------------\\\\
0=3-t^2\implies t^2=3\implies t=\sqrt{3}\implies t\approx \stackrel{seconds}{1.7} [/tex]
Answer:
3 seconds.
Step-by-step explanation:
We have been given that a punter kicks a football upward with an initial speed of 48 feet per second. Use the formula [tex]h=rt-16t^2[/tex] to find after how many minutes ball will hit the ground.
The ball will hit the ground, when height, h equals to 0.
[tex]h=48t-16t^2[/tex]
[tex]0=48t-16t^2[/tex]
[tex]-16t^2+48t=0[/tex]
[tex]-16t(t-3)=0[/tex]
Using zero product property, we will get:
[tex]-16t=0\text{ or }(t-3)=0[/tex]
[tex]t=0\text{ or }t-3=0[/tex]
[tex]t=0\text{ or }t=3[/tex]
Therefore, after 3 seconds ball will hit the ground.
