ANSWER
[tex]\begin{equation*} 187.62\text{ }ft\/s \end{equation*}[/tex]
EXPLANATION
To find the initial velocity that the object must have, we have to apply one of Newton's equations of motion:
[tex]v^2=u^2-2gs[/tex]
where v = final velocity
u = initial velocity
g = acceleration due to gravity = 32 ft/s/s
s = distance/height traveled
Since the object reaches the top of the monument, its final velocity is 0 ft/s.
Substitute the given values into the equation and solve for u:
[tex]\begin{gathered} 0^2=u^2-2*32*550 \\ \\ 0=u^2-35200 \\ \\ u^2=35200 \\ \\ u=\sqrt{35200} \\ \\ u=187.62\text{ }ft\/s \end{gathered}[/tex]
That is the initial velocity that the object must be thrown at.
