Question

A baseball is hit, following a path represented by x = 135t and y = 3.3 + 38t − 16t 2 for 0 ≤ t ≤ 3. Write a rectangular equation to represent the plane curve.

Answer 1

Rectangular Equation

We are given the parametric equations:

$\begin{gathered} x=135t \\ y=-16t^2+38t+3.3 \end{gathered}$

From the first equation, solve for t:

$t=\frac{x}{135}$

Substitute in the second equation:

$\begin{gathered} \\ y=-16(\frac{x}{135})^2+38(\frac{x}{135})+3.3 \end{gathered}$

Operating:

$\begin{gathered} \\ y=\frac{-16x^2}{18225}+\frac{38x}{135}+3.3 \end{gathered}$

Multiply both sides of the equation by 18225:

$18225y=-16x^2+5130x+60142.5$