Solve the problem. Round your answer to the nearest tenth, when appropriate.
-A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is given by $s(t)=16 t^{2}+32 t$, where $s$ is in feet. How long will it take the ball to fall $160 \mathrm{ft}$ ?
A) $2.3 \mathrm{sec}$
B) $3.2 \mathrm{sec}$
C) $5.3 \mathrm{sec}$
D) $2.1 \mathrm{sec}$

Question

Quizplus · Accepted Answer

To find the time it takes for the ball to fall 160 ft, set $s(t) = 160$ and solve for $t$:  $16t^2 + 32t = 160$  $16t^2 + 32t - 160 = 0$  Divide the entire equation by 16:  $t^2 + 2t - 10 = 0$  Using the quadratic formula $t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 1$, $b = 2$, and $c = -10$:  $t = \frac{-2 \pm \sqrt{2^2 - 4 \cdot 1 \cdot (-10)}}{2 \cdot 1}$  $t = \frac{-2 \pm \sqrt{4 + 40}}{2}$  $t = \frac{-2 \pm \sqrt{44}}{2}$  $t = \frac{-2 \pm 6.633}{2}$  The positive solution is $t = \frac{4.633}{2} = 2.3165$, rounded to the nearest tenth is $2.3$ seconds.

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

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