Chapter 11.2, Problem 63E

To determine

To simulate the baseball problem in example 6 and use the parametric graphing mode on your calculator.

Explanation of Solution

A sketch of the parametric function $\begin{array}{l}\mathrm{X}=110\mathrm{T}\cos ({60}^{\circ })\\ \mathrm{Y}=110\mathrm{T}\sin ({60}^{\circ })\end{array}$ is shown below.

  

This function gives the slope of the ball at its initial trajectory, but does not account for gravity in the y − component. In order to adjust the graph so that gravity is a factor, $-16{\mathrm{T}}^2$ needs to be added to the y − component.

A sketch of the parametric function $\begin{array}{l}\mathrm{X}=110\mathrm{T}\cos ({60}^{\circ })\\ \mathrm{Y}=110\mathrm{T}\sin ({60}^{\circ })-16{\mathrm{T}}^2\end{array}$ is shown below.

  

The following table shows T-values near 5, and you can see that the ball hits the ground some-time between $\mathrm{T}=5.95$ and $\mathrm{T}=6$