# Conservation of Momentum of astronaut

1. Homework Statement
An astronaut is a distance $$L$$ from her spaceship, and is at rest with respect to the ship, when she discovers that her tether has broken. She tosses a wrench with a speed of $$V_W$$ in the opposite direction of the ship to propel herself back to the ship. The astronaut has mass $$M_A$$, and the wrench has mass $$M_W$$.

How long does it take her to reach the ship in terms of $$L$$, $$M_A$$, $$M_W$$ and $$V_W$$?

2. Homework Equations

Conservation of momentum: $$P_i=P_f$$
I don't know what equation to use to find time? $$v= d/t$$?

3. The Attempt at a Solution
$$(M_A+M_W)(V_i)=(M_W)(V_Wf)-(M_A)(V_Af)$$
$$V_Af=(M_f)(V_Wf)/(M_A)$$

$$t=d/v$$
$$t=(L)(M_A)/(M_W)(V_Wf)$$

Is that right? Thanks.

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