Chapter 3.4, Problem 12AE

Analyzing the Motion of a Projectile A projectile is fired at an inclination of ${45}^{\circ }$ to the horizontal, with a muzzle velocity of 100 feet per second. The height $h$ of the projectile is modeled by

$h\left(x\right)=\frac{-32x^2}{{\left(100\right)}^2}+x$

where $x$ is the horizontal distance of the projectile from the firing point.

(a) At what horizontal distance from the firing point is the height of the projectile a maximum?

(b) Find the maximum height of the projectile.

(c) At what horizontal distance from the firing point will the projectile strike the ground?

(d) Using a graphing utility, graph the function $h$ $0\le x\le 350$.

(e) Use a graphing utility to verify the results obtained in parts (b) and (c).

(f) When the height of the projectile is 50 feet above the ground, how far has it traveled horizontally?