Solve the problem.
-A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is $s = 16 t ^ { 2 } + 32 t$, where $s$ is in feet. How long (to the nearest tenth) will it take the ball to fall 152 feet?
A) $2.2 \mathrm { sec }$
B) $2.0 \mathrm { sec }$
C) $4.8 \mathrm { sec }$
D) $3.1 \mathrm { sec }$

Question

Quizplus · Accepted Answer

To find the time it takes for the ball to fall 152 feet, set $s = 152$ and solve for $t$: $152 = 16t^2 + 32t$. Rearranging gives $16t^2 + 32t - 152 = 0$. Dividing the entire equation by 16 gives $t^2 + 2t - 9.5 = 0$. Using the quadratic formula, $t = \frac{-2 \pm \sqrt{(2)^2 - 4(1)(-9.5)}}{2(1)}$, which simplifies to $t = \frac{-2 \pm \sqrt{4 + 38}}{2}$, or $t = \frac{-2 \pm \sqrt{42}}{2}$. The positive solution is approximately $2.2$ seconds.

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

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