Chapter 6.3, Problem 6E

Reminder Round all answers to two decimal places unless otherwise indicated.

The Cannon with a Different Muzzle Velocity If the cannonball from example $6.7$ is fired with a muzzle velocity of $370\text{ feet per second}$, it will follow the graph of

$h=x-32{\left(\frac{x}{370}\right)}^2$,

where distances are measured in feet.

a. Plot the graph of the flight of the cannonball.

b. Find the height of the cannonball $3000\text{feet}$ downrange.

c. By looking at the graph of $h$, determine whether $\frac{dh}{dx}$ is positive or negative at $3000\text{feet}$ downrange.

d. Calculate $\frac{dh}{dx}$ at $3000\text{feet}$ downrange and explain what this number means in practical terms.