Answer:
The rocket will hit the ground after about 8.20 seconds.
Step-by-step explanation:
The height of the rocket <em>y</em>, in feet, <em>x</em> seconds after launch is modeled by the equation:
We want to find the time at which the rocket will hit the ground.
If it hits the ground, the height of the rocket <em>y</em> will be 0. Thus:
We can solve for <em>x</em>. Factoring (if possible at all) or completing the square can be tedious, so we can use the quadratic formula:
In this case, <em>a</em> = -16, <em>b</em> = 121, and <em>c </em>= 83. Substitute:
Simplify:
Divide everything by -1 and simplify the square root. The plus/minus will remain unchanged:
Therefore, our two solutions are:
Since time cannot be negative, we can ignore the second solution.
Therefore, the rocket will hit the ground after about 8.20 seconds.