Solve the problem.
-If an object is propelled upward from a height of 32 feet at an initial velocity of 80 feet per second, then its height after $t$ seconds is given by the equation $\mathrm { h } ( \mathrm { t } ) = - 16 \mathrm { t } ^ { 2 } + 80 \mathrm { t } + 32$, where height is in feet. After how many seconds will the object reach a height of 132 feet?
A) $1.3 \mathrm { sec }$
B) $10 \mathrm { sec }$
C) $2.5 \mathrm { sec }$
D) $5 \mathrm { sec }$

Question

Quizplus · Accepted Answer

To find when the object reaches a height of 132 feet, set $h(t) = 132$ and solve for $t$: $132 = -16t^2 + 80t + 32$. Rearranging gives $16t^2 - 80t + 100 = 0$, which simplifies to $t^2 - 5t + 6.25 = 0$. Factoring or using the quadratic formula yields $t = 2.5$ seconds.

Solve the Problem ttt Seconds Is Given by the Equation h(t)=−16t2+80t+32\mathrm { h } ( \mathrm { t } ) = - 16 \mathrm { t } ^ { 2 } + 80 \mathrm { t } + 32h(t)=−16t2+80t+32

Solve the Problem $t$ Seconds Is Given by the Equation $\mathrm { h } ( \mathrm { t } ) = - 16 \mathrm { t } ^ { 2 } + 80 \mathrm { t } + 32$