In order to calculate the initial velocity required, we can use Torricelli's equation:
[tex]V^2=V_o^2+2\cdot a\cdot d[/tex]
Where V is the final velocity, Vo is the initial velocity, a is the acceleration and d is the distance traveled.
The minimum initial velocity will occur when the final velocity at the position 550 m is zero, so we have:
[tex]\begin{gathered} 0^2=V_o^2+2\cdot(-32)\cdot550\\ \\ 0=V_o^2-64\cdot550\\ \\ V_o^2=35200\\ \\ V_o=187.62\text{ ft/s} \end{gathered}[/tex]
