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**[SOLVED] Conservation of linear momentum/Galilean relativity problem**

## Homework Statement

A 45-kg girl is standing on a plank that has a mass of 150 kg. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless supporting surface. The girl begins to walk along the plank at a constant velocity of 1.5 m/s

*relative to the plank*.

(a) What is her velocity relative to the ice surface?

(b) What is the velocity of the plank relative to the ice surface?

## Homework Equations

[tex]m_1v_1 = m_2v_2[/tex]

[tex]\overrightarrow{p_{1i}} + \overrightarrow{p_{2i}} = \overrightarrow{p_{1f}} + \overrightarrow{p_{2f}}[/tex]

[tex]\overrightarrow{r}' = \overrightarrow{r} - \overrightarrow{u}t[/tex]

[tex]\overrightarrow{v}' = \overrightarrow{v} - \overrightarrow{u}[/tex]

## The Attempt at a Solution

mass of girl:

[tex]m_g = 45 kg[/tex]

mass of plank:

[tex]m_p = 150 kg[/tex]

velocity of girl relative to plank:

[tex]v_{gp} = 1.5 m/s[/tex]

velocity of plank relative to girl:

[tex]v_{pg} = ?[/tex]

conservation of momentum:

[tex]m_gv_{gp} = m_pv_{pg} \Rightarrow[/tex]

[tex]v_{pg} = \frac{m_gv_{gp}}{m_p} = \frac{(45 kg)(1.5 m/s)}{150kg} = 0.450 m/s[/tex]

So I have the velocity of the plank relative to the girl; but I have no idea how to find the velocity of the girl or the plank relative to the ice. Can you help? Thank you.