Question

A Theme park wants to build a roller coaster with the maximum velocity of 33.5 MS (75 mph ) how high Must the first hill be in order to reach the maximum velocity?

Answer 1

We will determine the height as follows:

First, we determine the time it will take to get from 0m/s to 33.5m/s using gravity, that is:

`\begin{gathered} 33.5m/s=(0m/s)+(9.8m/s^2)t\Rightarrow t=(33.5m/s)/(9.8m/s^2) \\ \\ \Rightarrow t=(335)/(98)s \end{gathered}`

Now, we determine the height of the roller coaster:

`\begin{gathered} h=(0m/s)((335)/(98)s)+(1)/(2)(9.8m/s^2)((335)/(98)s)^2\Rightarrow h=(22445)/(392)m \\ \\ \Rightarrow h\approx57.26m \end{gathered}`

So, the height of the roller coaster must be approximately 57.26 m.