Respuesta :
Answer:
It would take approximately 6.50 second for the cannonball to strike the ground.
Step-by-step explanation:
Consider the provided function.
[tex]h(t)=-4.9t^2+30.5t+8.8[/tex]
We need to find the time takes for the cannonball to strike the ground.
Substitute h(t) = 0 in above function.
[tex]-4.9t^2+30.5t+8.8=0[/tex]
Multiply both sides by 10.
[tex]-49t^2+305t+88=0[/tex]
For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are: [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute a = -49, b = 305 and c=88
[tex]t=\frac{-305+\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}=-\frac{-305+\sqrt{110273}}{98}\\t = \frac{-305-\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}= \frac{305+\sqrt{110273}}{98}[/tex]
Ignore the negative value of t as time can't be a negative number.
Thus,
[tex]t=\frac{305+\sqrt{110273}}{98}\approx6.50[/tex]
Hence, it would take approximately 6.50 second for the cannonball to strike the ground.
