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=(x)/(135)`

Substitute in the second equation:

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

Operating:

`\begin{gathered} \\ y=(-16x^2)/(18225)+(38x)/(135)+3.3 \end{gathered}`

Multiply both sides of the equation by 18225:

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