Suppose the position function for a free-falling object on a certain planet is given by $s ( t ) = - 12 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$. A silver coin is dropped from the top of a building that is 1372 feet tall. Find the time required for the coin to reach ground level. Round your answer to the three decimal places.
A) $2.849 \mathrm { sec }$
B) $10.273 \mathrm { sec }$
C) $10.693 \mathrm { sec }$
D) $3.087 \mathrm { sec }$
E) $10.091 \mathrm { sec }$

Question

Quizplus · Accepted Answer

We are given the position function as $s ( t ) = - 12 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$. We know that when the coin hits the ground, its height is 0. So, we set $s(t)$ to 0 and solve for t.

\begin{align*}
s(t) &= -12t^2 + v_0t + s_0 \
0 &= -12t^2 + v_0t + s_0 \
\end{align*}

We are given that the coin is dropped from the top of a building that is 1372 feet tall, so we know the initial height is 1372 feet, i.e. $s(0) = 1372$ and the initial velocity is 0, i.e. $v_0 = 0$. Therefore, we have

\begin{align*}
0 &= -12t^2 + 0t + 1372 \
t^2 &= \frac{1372}{12} = 114.333... \
t &= \sqrt{114.333...} \approx 10.693
\end{align*}

Rounding to three decimal places, we get the answer as $10.693$ seconds, which is choice C.

Suppose the Position Function for a Free-Falling Object on a Certain