Question

In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is 1.44 m. The mug slides off the counter and strikes the floor 1.60 m from the base of the counter.

(a) With what velocity did the mug leave the counter?

------- m/s
(b) What was the direction of the mug's velocity just before it hit the floor?

------- ° (below the horizontal)

Answer 1

Find the time for a 1.44 m free fall
s = 1/2 gt²
t = √(2s/g)
t = √(2*1.44/9.81)
t = 0.54 s

Vertical Velocity:
Find the final velocity for the free fall through 1.44 m
v = √(2gs)
v = √(2*9.81*1.44)
v = 5.31 m/s

Horizontal velocity leaving the counter:
the horizontal distance is 1.6 m in 0.54 s
v = s/t
v = 1.6/0.54 = 2.96 m/s.

Direction of final velocity below horizontal:
angle = tan^-1(vertical velocity/horizontal velocity)
angle = tan^-1(5.31/2.96)
angle = 60.86°