Question

a model rocket is launched from the top of a building. the height (in meters) of the rocket above the ground is given by h(t)= - 5t²+30t + 10, where t is the time since the rocket was launched. what is the rockets maximum height? maximum height h = 47.5 meters

Explanation:

Step1: Identify the function type

The height function $h(t)= - 5t^{2}+30t + 10$ is a quadratic function in the form $y = ax^{2}+bx + c$ where $a=-5$, $b = 30$ and $c = 10$.

Step2: Find the time at which maximum occurs

The time $t$ at which the maximum of a quadratic function $y=ax^{2}+bx + c$ occurs is given by $t=-\frac{b}{2a}$. Substituting $a=-5$ and $b = 30$ into the formula, we get $t=-\frac{30}{2\times(-5)}=\frac{-30}{-10}=3$.

Step3: Calculate the maximum height

Substitute $t = 3$ into the height - function $h(t)$. So $h(3)=-5\times(3)^{2}+30\times3 + 10=-5\times9+90 + 10=-45+90 + 10=47.5$.

Answer:

$47.5$ meters