Answer:
8.5 seconds to hit the ground
Step-by-step explanation:
A soccer ball is thrown upward from the top of a 204 foot high building at a speed of 112 feet per second.
[tex]h(t)=-16t^2+V_0t+h_0[/tex]
Vo is the speed 112 feet per second
h0 is the initial height = 204 foot
So the equation becomes
[tex]h(t)=-16t^2+112t+204[/tex]
When the soccer ball hit the ground then the height becomes 0
[tex]0=-16t^2+112t+204[/tex]
Apply quadratic formula
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]t=\frac{-112+\sqrt{112^2-4 (-16) \cdot 204}}{2(-16)}[/tex]
[tex]t=\frac{-112+\sqrt{25600}}{-32}=-1.5[/tex]
[tex]\frac{-112-\sqrt{25600}}{-32}=8.5[/tex]
time cannot be negative
so it takes 8.5 seconds to hit the ground
