Solve the problem.
-A rock is propelled upward from the top of a building 160 feet tall at an initial velocity of 48 feet per second. The function that describes the height of the rocket in terms of time $t$ is $s ( t ) = - 16 t ^ { 2 } + 48 t + 160$. Determine the maximum height that the rock reaches.
A) $196 \mathrm { ft }$
B) $166 \mathrm { ft }$
C) $179 \mathrm { ft }$
D) $213 \mathrm { ft }$

Question

Quizplus · Accepted Answer

The maximum height can be found by using the vertex formula for a quadratic equation $s(t) = -16t^2 + 48t + 160$. The time at which the maximum height is reached is given by $t = -\frac{b}{2a}$, where $a = -16$ and $b = 48$. Thus, $t = -\frac{48}{2(-16)} = 1.5$ seconds. Substituting $t = 1.5$ into the equation gives $s(1.5) = -16(1.5)^2 + 48(1.5) + 160 = 196$ feet.

Solve the Problem ttt Is s(t)=−16t2+48t+160s ( t ) = - 16 t ^ { 2 } + 48 t + 160s(t)=−16t2+48t+160

Solve the Problem $t$ Is $s ( t ) = - 16 t ^ { 2 } + 48 t + 160$