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An astronaut is conducting repairs on a satellite 50.0m from a space shuttle. Her mass is 120kg (including space suit) and she is using a 0.5kg spanner. She realises that she only has 5 minutes oxygen supply remaining. With what velocity must the spanner be thrown for her to return to the shuttle safely.

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closed as off topic by David Z May 18 '11 at 19:21

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Hint: 1st: velocity $ v=d/t $, substitute in distance and time to find the required velocity. 2nd: momentum is conserved. $ p=mv $ for both the astronaut and the spanner, equate them. Rearrange to solve. All the best ;) –  qftme May 18 '11 at 12:21
    
thanks alot. i appreciate your help:] –  Quinny May 20 '11 at 10:56
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1 Answer

To start off, I assume that the throw is instantaneous, and that it's ok to arrive in exactly 5 minutes (no time for the airlock!). That means that the required velocity is quite easily:

$$\frac{50 m}{5 minutes \frac{ 60 seconds }{ minute} } = 0.166 \frac{m}{s}$$

For the throw, we have $(Mv)_1=(Mv)_2$, and the ratios of the masses are know to be $M_1/M_2=120/0.5=240$, so from that equation the ratios of velocities has to be reverse of that.

$$v_2=v_1 \frac{M_1}{M_2}=0.166 \frac{m}{s} 240 = 40 \frac{m}{s}$$

And I take it that this would not be feasible and that she would need to think of another plan. Granted, I think that even if you could do it, aiming would be difficult since 50.0 m is a long way and I don't know how much practice she has in space sports. But then again, maybe this is just unlikely enough to make for a good movie plot.

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Actually, the word record baseball throw is in the neighborhood of $100 mph = 44 m/s$. A baseball is about $140 g$. Thus, it's possible that the throw required to get our heroic astronaut to safety may not be doable by a human. I welcome suggestions for better examples than that of the baseball. –  AlanSE May 18 '11 at 14:26
    
A little nitpicky perhaps but using the same $m$ for mass and meters could be a little confusing. –  qftme May 18 '11 at 14:44
    
Changed to using $M$ for mass as per qftme's suggestion. oh oh, and I've got it! She throws the spanner in order to get herself to the satellite, then kicks off the satellite to get back to the ship, which can easily be done in time. ^^ –  AlanSE May 18 '11 at 16:13
    
for future reference, we prefer that complete answers not be given out for homework questions like this one. –  David Z May 18 '11 at 19:22
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