Question

35) ROLLER COASTER Starting from a stationary position, the velocity v of a roller coaster in feet per second at the bottom of a hill can be approximated by v = √64h, where h is the height of the hill in feet. a. Simplify the equation. b. Determine the velocity of a roller coaster at the bottom of a 134-foot hill.

Answer 1

Given the following function:

$v(h)=\sqrt[]{64h}$

we can separate both factors inside the square root to get:

$\begin{gathered} v(h)=\sqrt[]{64h}=\sqrt[]{64}\cdot\sqrt[]{h}=8\cdot\sqrt[]{h} \\ \Rightarrow v(h)=8\cdot\sqrt[]{h} \end{gathered}$

next, to determine the velocity at the bottom of the hill, we can make h = 134, and evaluate the function:

$\begin{gathered} h=134 \\ \Rightarrow v(134)=8\cdot\sqrt[]{134}=8(11.58)=92.64 \\ v(h)=92.64\frac{ft}{s} \end{gathered}$

therefore, the velocity at the bottom of a 134 foot hill is 92.64 ft/s