Question

a rocket is launched in the air and its height, in feet, is modeled by the function h. here is a graph representing h. select all true statements about the situation. the rocket is launched from a height less than 20 feet above the ground. the rocket is launched from exactly 20 feet above the ground. the rocket reaches its maximum height after about 160 seconds. the rocket reaches its maximum height after about 3 seconds. the maximum height of the rocket is about 160 feet.

Explanation:

Step1: Check launch - height

When time \(t = 0\), the height \(h(0)\) is close to \(0\), so the rocket is launched from a height less than 20 feet above the ground.

Step2: Check time - to - maximum

The vertex of the parabolic - shaped height - time graph occurs at \(t\approx3\) seconds.

Step3: Check maximum height

The \(y\) - value at the vertex of the graph is approximately \(h = 160\) feet.

Answer:

The rocket is launched from a height less than 20 feet above the ground.
The rocket reaches its maximum height after about 3 seconds.
The maximum height of the rocket is about 160 feet.