<p>If the treadmill matches the plane’s speed relative to the treadmill itself, we essentially have |V<em>t| = |V</em>p| + |V<em>t|. It looks like there is an infinity that’s going to come into play, but the (apparent) iteration converges: I now see your issue, you are falling into Zeno’s paradox. For any |V</em>p| (this is the speed of the plane relative to the ground), there is some finite |V_t| that will stop the plane all together (relative to the ground). When the treadmill reaches this speed, the equation holds.</p>