A bartender gives a full mug of beer an initial speed \(v_{\text {full }}\), and the mug stops in front of a patron sitting at the end of the bar. This patron later asks for a mug only half full. The bartender stands at the same position as when she sent the full mug to the patron and gives the mug an initial speed \(v_{\text {half }}\). If the mug is to again stop in front of the patron, which is true: \(v_{\text {half }}v_{\text {full }}\) ?