Question

Bartender slides a beer mug at 1.1 m/s towards a customer at the end of the bar which is 1.8 m tall. The customer makes a grab for the mug and misses and mug sails at the end of the bar. a) How far away from the end of the bar does the mug hit the floor

Answer 1

Δx = 0.7 m

Step-by-step explanation:

• Once the mug is moving in the horizontal direction, it keeps moving at the same speed of 1.1 m/s, due to no other force acts on it in this direction.
• Since the horizontal and vertical movements are independent each other (due to they are mutually perpendicular), in the vertical direction, the initial speed is just zero.
• In the vertical direction, the mug is accelerated by the force of gravity at all times, with a constant value of 9.8 m/s2, aimed downward.
• So, we can use the following kinematic equation in order to get the time passed from the instant that the mug left the bar, until it hit the floor, as follows:
• 
  `\Delta y = (1)/(2) * g* t^(2) = (1)`
• where Δy = 0-1.8m = -1.8m, g= -9.8m/s2.
• Replacing these values in (1) and solving for t, we get:

`t = \sqrt{(2*1.8m)/( 9.8m/s2) } = 0.6 s (2)`

• Now, since the mug obviously finishes its horizontal trip at this same time (hitting ground), we can find the horizontal distance traveled, just applying the definition of average speed, as follows:

`\Delta x = v_(o) * t = 1.1 m/s* 0.6 s = 0.7 m (3)`