Question

select the correct solution set. determine the time when the rocket will be more 60 feet above the ground. (0, 3.5) ∪ (4, 7.6) (3.5, 4) 0, 3.5 ∪ 4, 7.6 3.5, 4

Explanation:

Since no height - time function for the rocket is given, we assume a general quadratic height - time function of the form $h(t)=at^{2}+bt + c$ (where $h(t)$ is the height of the rocket at time $t$, and $a,b,c$ are constants). To find when $h(t)>60$, we set up the inequality $at^{2}+bt + c>60$, or $at^{2}+bt+(c - 60)>0$.

If we assume that we have already found the roots of the corresponding quadratic equation $at^{2}+bt+(c - 60)=0$ to be $t_1$ and $t_2$ ($t_10$ is either $tt_2$ (if $a>0$) or $t_1

However, since time $t\geq0$, we consider the valid intervals within the non - negative real numbers.

Let's assume we have found the roots of the quadratic equation related to the height inequality and determined the intervals.

If the rocket's height is modeled by a quadratic function and we have found the times when the height is exactly 60 feet as $t = 3.5$ and $t = 4$, and the parabola opens downwards (which is typical for a rocket's height - time function as it goes up and then comes down), the rocket is above 60 feet when $3.5

Step1: Analyze height - time model

Assume quadratic height - time model.

Step2: Find roots of related equation

Find roots for height = 60.

Step3: Determine valid interval

For downward - opening parabola, height > 60 between roots.

Answer:

$(3.5,4)$