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

[Glyper]

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?

 

[Basic_Physics]

Well the eqaution implies that: mom boat - mom rock = 0
Why would that be?

 

[Doc Al]

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

 

[Glyper]

Oh, I see. Thank you a lot!

 

[Nickie]

I can explain the formula you have written and how it applies to this situation. The formula you have written is known as the conservation of momentum equation, which states that the total momentum of a system remains constant unless acted upon by an external force. In this case, the system consists of the man, the boat, and the rock.

The initial momentum of the system is given by m1v1 (mass of the rock multiplied by its velocity) and this is equal to the final momentum of the system, which is given by m2v2 (mass of the man and boat combined multiplied by their common velocity v2). This is because in this scenario, the only external force acting on the system is the throw of the rock, which does not affect the total mass of the system. Therefore, the conservation of momentum equation can be applied to solve for v2.

I hope this explanation helps you understand the formula and its application in this scenario. If you have any further questions, please let me know.