# Conservation of Momentum of astronaut

1. Apr 10, 2008

### jonnejon

1. The problem statement, all variables and given/known data
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. Relevant 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.

Last edited: Apr 10, 2008
2. Apr 10, 2008

### Dr. Jekyll

Seems correct to me.