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.

Question

Quizplus · Accepted Answer

The bottle moves 22 cm backward in 0.44 s, so its velocity is 50 cm/s. By conservation of momentum, the cork's velocity is 500 times that of the bottle, so 25000 cm/s. In 0.44 s, the cork travels 0.44 * 25000 = 11000 cm = 110 m. Since the bottle moved 22 cm backward, the cork lands 110 m - 22 cm = 10978 cm = 109.78 m from the original position.

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