Chapter 3.3, Problem 86AYU

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

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

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

At what horizontal distance from the firing point is the height of the projectile

Find the maximum height of the projectile.

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

Graph the function $h$ $0\le x\le 350$.

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

When the height of the projectile is $50$ feet above the ground, how far has it travelled horizontally?