Chapter 13.3, Problem 17ES

(a)

To determine

To calculate: The value of partial derivative of $r$ with respect to $v$ , when $v=80\text{ ft/s}$ and $\theta =40°$ from the table below. Where, $r$ is the horizontal range of the baseball in $\left(\text{ft}\right)$ , $v$ is the initial velocity in $\left(\text{ft/s}\right)$ , at which the ball is thrown, and $\theta$ is the angle above the horizontal at which the ball is thrown.

$\begin{array}{|ccccc|}\hline & 75& 80& 85& 90\\ 35& 165& 188& 212& 238\\ 40& 173& 197& 222& 249\\ 45& 176& 200& 226& 253\\ 50& 173& 197& 222& 249\\ \hline\end{array}$

(b)

To determine

To calculate: The value of partial derivative of $r$ with respect to $\theta$ , when $v=80\text{ ft/s}$ and $\theta =40°$ from the table below. Where, $r$ is the horizontal range of the baseball in $\left(\text{ft}\right)$ , $v$ is the initial velocity in $\left(\text{ft/s}\right)$ , at which the ball is thrown, and $\theta$ is the angle above the horizontal at which the ball is thrown.

$\begin{array}{|ccccc|}\hline & 75& 80& 85& 90\\ 35& 165& 188& 212& 238\\ 40& 173& 197& 222& 249\\ 45& 176& 200& 226& 253\\ 50& 173& 197& 222& 249\\ \hline\end{array}$