A model rocket is launched from a raised platform at a speed of 144 feet per second. Its height in feet is given by $h ( t ) = - 16 t ^ { 2 } + 144 t + 20$ (t = seconds after launch). After how many seconds does the object reach its maximum height?
A) 2.25 seconds
B) 20 seconds
C) 4.5 seconds
D) 6.5 seconds

Question

Quizplus · Accepted Answer

The maximum height of a projectile in a quadratic equation of the form $h(t) = at^2 + bt + c$ is found at $t = -\frac{b}{2a}$. Here, $a = -16$ and $b = 144$, so $t = -\frac{144}{2(-16)} = 4.5$ seconds.

A Model Rocket Is Launched from a Raised Platform at a Speed