A rock is propelled upward from the top of a building 270 feet tall at an initial velocity of 168 feet per second. The function that describes the height of the rocket in terms of time t is $( t ) = - 16 t ^ { 2 } + 168 t + 270$ Determine the
Time at which the rock reaches its maximum height.
A) 8.4 sec
B) 10.5 sec
C) 4.2 sec
D) 5.25 sec

Question

Quizplus · Accepted Answer

The maximum height is reached at the vertex of the parabola, which occurs at $ t = -\frac{b}{2a} $. Here, $ a = -16 $ and $ b = 168 $, so $ t = \frac{-168}{2 \times -16} = 5.25 $ seconds.

A Rock Is Propelled Upward from the Top of a Building