A rock from a boat - could you help me understand?

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The discussion focuses on a physics problem involving a man on a boat throwing a rock and the resulting velocity of the boat. The key equation derived is based on the conservation of momentum, stating that the momentum before and after the rock is thrown must be equal. The formula v2 = (m1*v1)/m2 is used to calculate the boat's velocity, where m1 is the mass and velocity of the rock, and m2 is the mass of the man and boat. The principle of conservation of momentum is emphasized, explaining that the total momentum remains zero if the system starts at rest. Understanding this concept clarifies why the equation works in this scenario.
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Homework Statement



A man on a boat throws behind him a rock of mass m1=2kg with a velocity of v1=18m/s. The mass of a man with a boat is m_2=90kg. What velocty v_2 will the boat go with?

Homework Equations



v2 = (m1*v1)/m2

The Attempt at a Solution



So I was upsent on the lesson where we were speaking about this and can't figure out where does the formula I wrote above come from. Why is it certain that m2v2=m1v1? Of course I know I can just plug the numbers inside and bam, I've got my answer but I'd rather know why does it work. Could you help?
 
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Well the eqaution implies that: mom boat - mom rock = 0
Why would that be?
 
It comes from the conservation of momentum. Since (presumably), the man and boat start out at rest, the total momentum is zero.

You might want to read this: Momentum Conservation in Explosions
 
Oh, I see. Thank you a lot!
 
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