Answer
Minimum initial velocity = 188 ft/sec (3 sig. fig.)
Work Step by Step
Use the kinematics equation $v^{2}=u^{2}+2as$ where v is velocity, u is initial velocity, a is acceleration and s is displacement.
Hence, for the object to just reach the top of the Washington Monument, it will have zero velocity once it reaches the top.
Setting v=0 and substituting a=-32 and s=550, we have
$0=u^{2}+2(-32)(550)$
Solving for u, we get u=±$\sqrt (35200)$
Hence u=187.6166 $\approx$ 188 ft/sec
