Mathematics

Problem

A projectile follows the parametric equations

x(t)=v_{0}t\cos\theta

and

y(t)=v_{0}t\sin\theta-\tfrac12 g t^{2}

, where

g=9.8\,\text{m/s}^{2}

. Let

v_{0}=20\,\text{m/s}

and

\theta=\frac{\pi}{4}

. Determine the value of

\displaystyle \frac{d^{2}y}{dx^{2}}

t=1\,\text{s}

and state whether the trajectory is steepening or flattening at that instant.