The classic momentum transfer between balls question

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The problem involves a 5.0-kg object exploding into two 2.5-kg pieces, with one piece moving at 4.0 m/s at a 50° angle north of east. The initial momentum of the system is calculated as 30 kg·m/s east. The conservation of momentum principle states that the total momentum before the explosion must equal the total momentum after the explosion. The user attempted to calculate the velocity of the second object but arrived at an incorrect result of 3.5 m/s at 48 degrees. A request for a detailed solution was made to identify the error in the calculations.
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Homework Statement



A 5.0-kg object has a velocity of 6.0 m/s, east when it explodes into two 2.5-kg objects.
After the explosion one of the objects has a velocity of 4.0 m/s at an angle of 50° north
of east. What is the magnitude and direction of the velocity of the other object after the
explosion

Homework Equations



P=MV

P(i) = P(f)

The Attempt at a Solution



P=2.5*4sin(50)

P(i) = 30
P(f) = 30

I got about 3.5m/s, at 48 degrees, which apparently is quite wrong.
 
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