How to Approach a Conservation of Linear Momentum Problem?

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Homework Statement


a 50kg man is standing at one end of a 25m long boat.if he starts running towards the other end,he attains a velocity of 2m/s on reaching the other end.if the mass of the boat is 200kg,what is the velocity of the boat?{can someone give me a hint as to how to approach such kind of problems}

Homework Equations


The Attempt at a Solution

 
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Start by writing an equation involving the momentum of the man and of the boat before and after he runs the 25m distance.
 
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To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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