Question

In a local bar, a customer slides an empty beer mug down the counter for a refill. The height of the counter is 1.2 m. The mug slides off the counter and strikes the floor 1.35 m from the base of the counter. Assume the mug moves in the positive x-direction. Give your answer in three significant figures.

a) With what velocity did the mug leave the counter?
b) What was the direction (in degrees and with respect to the horizontal) of the mug's velocity just before it hit the floor?

Answer 1

Part a can be solve using the equation of trajectory:

Y = x tana + (g*x^2)/ [2(V0^2)*(cos a)^2]

Where y is the height

X is the length

G is the acceleration due to gravity

Vo Is the initail velocity

a is the angle of trajectory

1.2 = 1.35 tan(0) + (9.81*1.35^2)/ [2(V0^2)*(cos 0)^2]

Solve for V0 = 2.729 m/s

b. can be solve using the formula

v = sqrt(2gy)

= sqrt ( 2*1.2*9.81)

= 4.852 m/s going down ( 0 degree from the horizontal)