Given:
The height of the rocket after t second taking off is given by the formula,
[tex]h=-2t^2+2t+12[/tex]Required:
We need to find the time when the rocket hit the ground.
Explanation:
We know that the greatest height is zero when the rocket hit the ground.
Substitute h =0 in the given equation to find the time when the rocket hit the ground.
[tex]-2t^2+2t+12=0[/tex]Divide both sides of the equation by (-2).
[tex]-\frac{2t^2}{-2}+\frac{2t}{-2}+\frac{12}{-2}=\frac{0}{-2}[/tex][tex]t^2-t-6=0[/tex][tex]Use\text{ }-t=-3t+2t.[/tex][tex]t^2-3t+2t-6=0[/tex]Taking out the common term.
[tex]t(t-3)+2(t-3)=0[/tex][tex](t-3)(t+2)=0[/tex][tex](t-3)=0,(t+2)=0[/tex][tex]t=3\text{ or t=-2.}[/tex]The time should not be of negative value.
[tex]t=3[/tex]