Chapter 3.3, Problem 85AYU

Analyzing the Motion of a Projectile A projectile is fired from a cliff $200$ feet above the water at an inclination of $45°$ to the horizontal, with a muzzle velocity of $50$ feet per second. The height $h$ of the projectile above the water is modeled by

$h(x)=\frac{-32x^2}{{50}^2}+x+200$

Where $x$ is the horizontal distance of the projectile from the face of the cliff.

At what horizontal distance from the face of the cliff is the height of the projectile a maximum?

Find the maximum height of the projectile.

At what horizontal distance from the face of the cliff will the projectile strike the water?

Graph the function $h$, $0\le x\le 200$.

Use a graphing utility to verify the solutions found in parts $(b)$ and $(c)$.

When the height of the projectile is $100$ feet above the water, how far is it from the cliff ?