If a pitcher throws a pitch at a velocity $v_0$, then the kinetic energy is $E_0=\frac 12mv_0^2$. If the pitcher releases the pitch from x feet higher, then we will suppose that he can readjust his delivery to hit the same spot over home plate with the same initial speed. But this time, there is added energy from the drop in height x, so the total kinetic energy is
Find the formula for $v$ in terms of $v_0$ and $x$. Then use a linear approximation to estimate the difference $v−v_0$, which is the gain in velocity due to the extra height.
could anyone provide hints? very confused.