Solve the problem. Give the answer to the nearest tenth.
-A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is $\mathrm { s } = 16 \mathrm { t } ^ { 2 } + 32 \mathrm { t }$, where $s$ is in feet. How long (to the nearest tenth) will it take the ball to fall 280 feet?
A) $3.3 \mathrm { sec }$
B) $10.9 \mathrm { sec }$
C) $3.1 \mathrm { sec }$
D) $4.2 \mathrm { sec }$

Question

Quizplus · Accepted Answer

To find the time it takes for the ball to fall 280 feet, set $s = 280$ and solve for $t$: $280 = 16t^2 + 32t$. Rearranging gives $16t^2 + 32t - 280 = 0$. Dividing the entire equation by 16 gives $t^2 + 2t - 17.5 = 0$. Using the quadratic formula, $t = \frac{-2 \pm \sqrt{(2)^2 - 4(1)(-17.5)}}{2(1)}$, which simplifies to $t = \frac{-2 \pm \sqrt{4 + 70}}{2}$, or $t = \frac{-2 \pm \sqrt{74}}{2}$. The positive solution is approximately $t = 3.3$ seconds, as the negative time would not make sense in this context.

Solve the Problem ttt In Seconds Is s=16t2+32t\mathrm { s } = 16 \mathrm { t } ^ { 2 } + 32 \mathrm { t }s=16t2+32t

Solve the Problem $t$ In Seconds Is $\mathrm { s } = 16 \mathrm { t } ^ { 2 } + 32 \mathrm { t }$