If an object is propelled upward from a height of 48 feet at an initial velocity of 64 feet per second, then its height after t seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 64 t + 48$ , where height is in feet. After how many
Seconds will the object reach a height of 112 feet?
A) 4 sec
B) 2 sec
C) 1 sec
D) 8 sec

Question

Quizplus · Accepted Answer

To find when the object reaches 112 feet, set $h(t) = 112$ and solve $-16t^2 + 64t + 48 = 112$. Simplifying gives $-16t^2 + 64t - 64 = 0$. Dividing by -16, we get $t^2 - 4t + 4 = 0$, which factors to $(t-2)^2 = 0$. Thus, $t = 2$ seconds.

If an Object Is Propelled Upward from a Height of 48