Answer:
[tex]t=0.64[/tex] and [tex]t=1.56[/tex] seconds
Step-by-step explanation:
[tex]h=1+11t-5t^2\\\\6=1+11t-5t^2\\\\0=-5+11t-5t^2\\\\0=-5t^2+11t-5\\\\t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\t=\frac{-11\pm\sqrt{11^2-4(-5)(-5)}}{2(-5)}\\\\t=\frac{-11\pm\sqrt{121-100}}{-10}\\ \\t=\frac{-11\pm\sqrt{21}}{-10}\\\\t=\frac{11}{10}\pm\frac{\sqrt{21}}{10}\\ \\t_1\approx0.64\\\\t_2\approx1.56[/tex]
Therefore, the values of t for which the ball's height is 6 meters is [tex]t=0.64[/tex] and [tex]t=1.56[/tex] seconds.
