A bartender slides a mug of root beer with mass m = 2.6 kg down a bar top of length L = 2.0 m to an inattentive patron who lets the mug fall a height h = 1.1 m to the floor. The bar top (Fig. P4.72) is smooth, but it still has a coefficient of kinetic friction µ_K= 0.080. 

(a) If the bartender gave the mug an initial velocity of 2.5 m/s, at what distance D from the bottom of the bar will the mug hit the floor? 

(b) What is the mug’s velocity (magnitude and direction) as it impacts the floor? 

(c) Draw velocity–time graphs for both the x and y directions for the mug, from the time the bartender lets go of the mug to the time it hits the floor. Ignore air drag.

Figure P4.72

y h