A rock is propelled upward from the top of a building 170 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 $s ( t ) = - 16 t ^ { 2 } + 168 t + 170$ Determine the
Maximum height that the rock reaches.
A) 630 ft
B) 592 ft
C) 579 ft
D) 611 ft

Question

Quizplus · Accepted Answer

The maximum height is found at the vertex of the parabola described by the function. The time at which the maximum height occurs is $ t = -\frac{b}{2a} = -\frac{168}{2(-16)} = 5.25 $ seconds. Plugging this back into the function gives $ s(5.25) = -16(5.25)^2 + 168(5.25) + 170 = 611 $ feet.

A Rock Is Propelled Upward from the Top of a Building