You are in mission control in Florida, supervising a probe on its way to Mars. The most recent report indicates that the probe will soon need to fire a quick burst of its booster rocket to increase its speed by \(5.2 \mathrm{~m} / \mathrm{s}\). You know that the spent fuel is ejected at a speed \(v_{\text {fuel }}=800 \mathrm{~m} / \mathrm{s}-v_{i}\), where \(v_{i}\) is the initial speed of the probe before firing, and that \(10 \%\) of the probe's inertia is currently fuel. Your main worry is whether enough fuel is left for landing maneuvers.