Find distance of Champagne cork

[Ienjoytrig...]

Homework Statement

A champagne bottle (diameter = 0.014 m) rests on its side on top of a frictionless table. The cork pops and the bottle slides backwards a distance of 0.3 meters in 0.72 seconds. If the bottle’s mass is 500 times greater than the cork’s mass, find the distance from the original position the cork will land on the table.

M= Bottle mass
m= cork mass

Homework Equations

v_bottle=d/t
p_bottle=Mv

The Attempt at a Solution

v_bottle= (.3m)/(.72s)= .42m/s
p_bottle= (.5kg)(.42 m/s) = .21 kg m/s

Obviously, I substituted M for .5kg making m= .001kg.

This is where I got stuck and I just need someone to help me with my next equation. From there I should be able to get through this.

 

[cupid.callin]

use conservation of momentum

 

[Ienjoytrig...]

Thanks, cupid.

Using CoM I got:

0kg m/s + 0kg m/s = (.21kg m/s) + p_{c, f}
p_{c, f} = -.21kg m/s

p=mv
-.21kg m/s = (.001kg)(v)
v = -210m/s

v = v_i + at
-210m/s = 0m/s + (-9.8m/s²)(t)
21.43s = t

x = x_i + v_it + 1/2 a t²
x = 0m + 0m/s(21.43s) + 1/2 (9.8m/s²)(21.43s)
x = 2550.3m

 

[cupid.callin]

Nice ;)