Contextual Applications of Differentiation · Superchallenge problem

A rocket's height is $h(t)=-16t^2+v_0t$ feet, for an unknown initial velocity $v_0$. Telemetry shows that at $t=3$ seconds the rocket is $288$ feet high and still rising. Find $v_0$, then use a linear approximation to estimate the rocket's height at $t=3.1$ seconds.