In a local bar, a customer slides an empty beer mug down the counter for a refil

Question

In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is 1.38 m. The mug slides off the counter and strikes the floor 0.80 m from the base of the counter (a) With what velocity did the mug leave the counter? Does the time required for the mug to hit the floor depend on its initial horizontal velocity? m/s (b) What was the direction of the mug's velocity just before it hit the floor? You appear to have correctly calculated the angle using your incorrect value from part (a).(below the horizontal)

Explanation / Answer

Height h = 1.38 m

Horizontal range   R = 0.8 m

Time taken to reach the ground t = [ 2h / g] = (2 x 1.38 / 9.8)^0.5 = 0.53s

           

We know R = v t

a) From this velocity of the mug leave the counter v = R /t

                                                                                = 0.8 / 0.53 = 1.51 m / s

(b). Horizontal component of velocity of the mug when it reachesthe ground   u = v

            u= 1.51 m / s

Vertical component of velocity when it reaches the ground U= gt

                                                                                                   = 9.8 x 0.53 = 5.194 m/s

So, the direction of the mug's velocity just before it hit thefloor = tan -1 ( U / u )

                                                                                                = tan -1 ( 5.194 / 1.51 )

                                                                                                      = 73.79 degrees with the horizontal .

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