Final answer:
To find how far the mug hits the floor from the bar, we calculate the falling time using the height of the bar and the acceleration due to gravity. Then, we multiply the calculated time by the horizontal velocity of the sliding mug. The mug lands approximately 74 cm away from the bar.
Step-by-step explanation:
If a bartender slides a beer mug at 1.50 m/s toward a customer at the end of a frictionless bar that is 1.20 m tall and the customer misses the mug, we can determine how far away from the bar the mug hits the floor by using the principles of projectile motion.
Because the bar height is 1.20 meters, we first need to find out how long it takes for the mug to reach the ground due to gravity. We'll use the equation for free fall: d = ½gt², where d is the distance, g is the acceleration due to gravity (9.81 m/s²), and t is time.
Solving for t, we get t = √(2d/g). Substituting d = 1.20 m, we find that t = √(2 * 1.20 m / 9.81 m/s²) = √(0.244) = 0.493 s approximately. Now that we have the time it takes to fall, we can calculate the horizontal distance traveled using the horizontal velocity: distance = velocity * time. The mug is sliding at a constant horizontal velocity of 1.50 m/s, so the distance is 1.50 m/s * 0.493 s = 0.740 m or 74 cm approximately. Thus, the mug hits the floor 74 cm away from the end of the bar.