Question

A rocket was launched into the air. The height of the rocket in feet, h is modeled by the followingequation, h(t) = -165 - 95t where t is the time in seconds after the rocket was launched. What was themaximum height of the rocket? How long does it take for the rocket its maximum height? How long didit take the rocket to hit the ground? Round to the nearest whole foot second.

Answer 1

The maximum height and the time elapsed to reach that maximum height is found locating the vertex of the quadratic function.

The equation:

`h(t)=-16t^2+95t`

has the form:

`f(t)=at^2+bt+c`

with a = -16, b = 95, and c = 0.

The vertex is found as follows:

`\begin{gathered} t=(-b)/(2a) \\ t=(-95)/(2\cdot(-16)) \\ t=3\text{ seconds} \end{gathered}`

The height is found evaluating the function at t = 3.