Conservation of Momentum of astronaut

[jonnejon]

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 $$V_W$$?

Homework Equations

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

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.

 

[Dr. Jekyll]

Seems correct to me.

 

[Moetasim]

Yes, your attempt at a solution is correct. To find the time it takes for the astronaut to reach the ship, we can use the equation t = d/v, where d is the distance (L) and v is the velocity. In this case, the velocity is the final velocity of the astronaut (V_Af), which we can find using the conservation of momentum equation. This equation states that the initial momentum (P_i) of the system (astronaut + wrench) is equal to the final momentum (P_f) of the system. We can set the initial momentum to be zero (since the astronaut is initially at rest) and solve for the final velocity of the astronaut.

Once we have the final velocity, we can plug it into the time equation to get the final answer in terms of L, M_A, M_W, and V_W. Your solution correctly takes into account the masses and velocities of both the astronaut and the wrench, and uses the correct equations to solve for the time. Well done!