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OSCOLPHYS$23\mathrm{.}4.$P$\mathrm{.}048.$

ASK YOUR TEACH

Prove that the trajectory of a projectile is parabolic, having the form $y=ax+b{x}^2.$ To obtain this expression, solve the equation $x=v_{0}t$ for $t$ and substitute it into the expression for $y=v_{0}t-(\frac{1}{2})g{t}^2.($These equations describe the $x$ and $y$ positions of a projectile that starts at the origin.$)$ You should obtain an equation of the form $y=ax+b{x}^2$ where a and $b$ are constants. $($Use the following as necessary: $g,,v_0,$ and $x.)$