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## Homework Statement

Two ice skaters have masses m

_{1}and m

_{2}and are initially stationary. Their skates are identical. They push against one another, as in Figure 7.11, and move in opposite directions with different speeds. While they are pushing against each other, any kinetic frictional forces acting on their skates can be ignored. However, once the skaters separate, kinetic frictional forces eventually bring them to a halt. As they glide to a halt, the magnitudes of their accelerations are equal, and skater 1 glides twice as far as skater 2. What is the ratio m

_{1}/m

_{2}of their masses?

## Homework Equations

m

_{1}v

_{1}+ m

_{2}v

_{2}= m

_{1}v

_{o1}+ m

_{2}v

_{o2}

v = x/t

## The Attempt at a Solution

At the beginning, the skaters are stationary:

m

_{1}v

_{1}+ m

_{2}v

_{2}= m

_{1}(0 m/s) + m

_{2}(0 m/s)

since distance has doubled for skater 2:

m

_{1}(x/t) + m

_{2}(2x/t) = 0 N(s)

Factoring out velocity

(x/t)(m

_{1}+ 2m

_{2}) = 0

Therefore, m

_{1}/m

_{2}= 1/2

What did I miss?