It takes approximately 4.8 seconds.
Using the equation h(t)=-16t²+76t+2 and the quadratic formula we have:
[tex]t=\frac{-76\pm \sqrt{76^2-4(-16)(2)}}{2(-16)}
\\
\\=\frac{-76\pm \sqrt{5776--128}}{-32}
\\
\\=\frac{-76\pm \sqrt{5776+128}}{-32}
\\
\\=\frac{-76\pm \sqrt{5904}}{-32}
\\
\\=\frac{-76\pm 76.8}{-32}=\frac{-76+76.8}{-32}\text{ or } \frac{-76-76.8}{-32}
\\
\\=\frac{0.8}{-32}\text{ or } \frac{-152.8}{-32}=-0.025\text{ or } 4.775[/tex]
The second value would be when it hits the ground again.
