S.O.S. Mathematics CyberBoard

I am currently studying for a physics exam and I came across this question in my book:

"An archer stands at rest on frictionless and fires a kg arrow horizontally at m/s by using a bow. The combined mass of the archer and the bow is kg. With what velocity does the archer move across the ice after firing the arrow?"

The solution given uses the law of conservation of momentum on the archer, the bow, and the arrow - and that's it. However, there are gravitational and normal forces that exist in this situation, so we can't do this without further reasoning. The book tries to justify using only the law of conservation of momentum by stating that no work is done by either of these forces. This doesn't make any sense to me seeing as total momentum is conserved when no external force acts on the system. I was thinking that one should use the law of conservation of momentum on the archer, the bow, the arrow, and the Earth in addition to the necessary 2D kinematics and the gravitational forces, etc.?

Any help would be appreciated.

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math puns are the first sine of madness
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Since one assumes the firing of arrow is instantaneous, there are no impulses and you can apply conservation of linear momentum.

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Would you consider the Earth in the system or would the system be the archer, the bow, and the arrow?

_________________
math puns are the first sine of madness
-JDR

"Ice" is physics code for "frictionless surface".

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I mistyped the question earlier, my b.





Hmmmm I originally meant "would one include the Earth in the law of conservation of momentum formula?"

But, this raises another question how would you do this with friction? I think that'd be really difficult seeing as you don't know any of the forces (except the friction force)?

_________________
math puns are the first sine of madness
-JDR

You just treat it as another force. None of this is terrible difficult, conservation of momentum works technically on a universal scale, not just a localized one. This problem wants you to just think about the archer and the arrow, as you get more pedantic problems will start occurring on larger scales.

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Awesome! Thanks Shadow and outermeasure!

_________________
math puns are the first sine of madness
-JDR