Answer:
T=5.9235 seconds
Step-by-step explanation:
[tex]H(T)= -4.9T^2+27.52T+8.9.[/tex]
The time it takes for the cannonball to strike the ground is the point at which H(T)=0
[tex]H(T)= -4.9T^2+27.52T+8.9.=0[/tex]
[tex]-4.9T^2+27.52T+8.9=0[/tex]
This is a quadratic equation and since we have a bunch of decimals we use the quadratic formula:
[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
a=-4,9, b=27.52, c=8.9
[tex]T=\dfrac{-27.52\pm\sqrt{(-27.52)^2-(4*-4.9*8.9)} }{2*-4.9}\\=\dfrac{-27.52\pm\sqrt{757.3504-(-174.44)} }{-9.8}\\=\dfrac{-27.52\pm\sqrt{931.7904} }{-9.8}\\=\dfrac{-27.52\pm30.53 }{-9.8}\\T=-0.3071 \:or\: 5.9235\\T=5.9235 seconds[/tex]
It takes 5.9235 seconds for the cannonball to strike the ground.
