An experienced bartender knows just the right initial speed of a glass of beer to get it

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An experienced bartender knows just the right initial speed of a glass of beer to get it to come to a stop in front any customer sitting along the bar. Say the initial speed needed to move a glass all the way to the end of the bar is \(v_{\text {cnd. }}\). In terms of \(v_{\text {end }}\), with what speed should an identical glass of beer be released if it is to stop at a customer sitting three-quarters of the way down the bar? (The kinetic energy converted to thermal energy because of friction is proportional to the distance the glass skids.)

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