(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An astronaut is a distance L from her spaceship, and it is at rest with respect to the ship, when she discovers that her tether is broken. She tosses a wrench with a spees V_{w}in the direction opposite that of the ship in ordr to propel herself back to the ship. The astronaut has a mass M_{A}, and the wrench has a mass M_{W}.

1) What is the initial momentum (before toss) of the astronaut + wrench system? What is the final momentum?

2) Use conservation of momentum to solve for the final speed. V_{A}of the astronaut relative to the ship, in terms of M_{A}, M_{W}

, and V_{w}.

3) How long does it take her to reach the ship? Express your answer in terms of L, M_{A}, m_{w}, and V_{W}?

4) How far has the wrench traveled from its original position when the astronaut reaches the ship? Express your answer in terms of L, M_{A}, and m_{W}?

2. Relevant equations

conservation of momentum: P_{i}=P_{F}if F_{net}=0

x=x_{0}+v_{x0}+1/2axt^{2}

3. The attempt at a solution

Please tell me if I've made any mistakes:

1) the initial momentum if zero since everything is at rest before she throws the wrench, and since it is an isolated system I have the following:

P_{F}=M_{a}(V_{a})+ m_{w}(v_{w})= P_{i}=0

2) final velocity is:

M_{a}V_{a}+m_{w}v_{w}=0

M^{a}v_{a}=-m_{w}v_{w}

v_{a}=-m_{w}v_{w}/m_{a}

3)how long it takes her to reach her ship:

x=x_{0}+v_{0x}+1/2at^{2}

(there is no acceleration due to gravity because they are in space)

0=L- (M_{w}V_{w}/m_{a}) t

L= (M_{w}V_{w}/m_{a}) t

I divided, inverted and multiplied, and came up with the following:

t= Lm_{a}/m_{w}v_{w}

4) I don't have any idea how to approach this part, and will appreciate any hints. Thank you.

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

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Conservation of momentum and astronaut

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