Question

theme park ride is descending on a parabolic path that can be approximated by the equation… (distance measured in feet.) If the horizontal component of its velocity is a constant 9 ft/s, find the rate of change of its elevationhenr = 30.

Answer 1

Solution

$\begin{gathered} y=-\frac{1}{90}x^2+75 \\ \frac{dy}{\text{dt}}=-\frac{1}{90}(2x)\frac{dx}{dt} \\ \\ \end{gathered}$$\begin{gathered} \frac{dy}{dt}=-\frac{1}{90}(2\times30)(9) \\ \\ \frac{dy}{dt}=-\frac{1}{90}(60)(9) \\ \\ \frac{dy}{dt}=-\frac{1}{9}(6)(9) \\ \\ \frac{dy}{dt}=-\frac{1}{9}(54) \\ \\ \frac{dy}{dt}=-6\text{ ft/s} \end{gathered}$