A 14-cm diameter champagne bottle rests on its side on top of a frictionless horizontal table. Suddenly, the cork pops and the bottle slides backward, covering a distance of $22.0 \mathrm {~cm}$ in $0.44 \mathrm {~s}$ If the mass of the bottle is 500 times the mass of the cork, find the distance from the original position that the cork will land on the table. Neglect air resistance and assume that the cork is very small compared to the bottle.
A) 3000 cm
B) 60 m
C) 85 m
D) 8.5 cm

Question

Quizplus · Accepted Answer

The bottle and cork system conserves momentum. The bottle moves 22 cm in 0.44 s, so its velocity is 50 cm/s. Since the bottle is 500 times the mass of the cork, the cork's velocity is 500 times that of the bottle, or 25000 cm/s. The cork travels for the same time, 0.44 s, so it covers a distance of 25000 cm/s * 0.44 s = 11000 cm or 110 m. Since the bottle moved 22 cm in the opposite direction, the cork lands 110 m - 0.22 m = 109.78 m from the original position, which is approximately 3000 cm.

A 14-Cm Diameter Champagne Bottle Rests on Its Side on Top