MATH SOLVE

5 months ago

Q:
# The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation h = -16t2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor. t mc001-1.jpg 0.87 s t mc001-2.jpg 4 s t = 8.5 s t = 16 s

Accepted Solution

A:

[tex]\bf h=-16t^2+255\implies h=-16t^2+0t+255
\\\\\\
~~~~~~~~~~~~\textit{quadratic formula}\\\\
\begin{array}{lcccl}
h=& -16 t^2& +0 t& +255\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\qquad \qquad
h= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a}
\\\\\\
h=\cfrac{-0\pm\sqrt{0^2-4(-16)(255)}}{2(-16)}\implies h=\cfrac{\pm\sqrt{16320}}{-32}
\\\\\\
h=\cfrac{\pm\sqrt{8^2\cdot 255}}{-32}\implies h=\cfrac{\pm 8\sqrt{255}}{-32}\implies h=\cfrac{\mp \sqrt{255}}{4}
\\\\\\
h\approx \mp 3.992179856[/tex]