Speed of Separation between 2 masses?

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The problem involves two astronauts and an object thrown in space, requiring the application of the law of conservation of momentum. Initially, both astronauts are at rest, and when one astronaut throws a 4.0 kg object at 10 m/s, it creates a recoil effect on the throwing astronaut. The momentum equation shows that the speed of separation between the two astronauts can be calculated by considering the recoil velocity of the first astronaut and the combined velocity after the second astronaut catches the object. The correct approach involves calculating the recoil velocity and then using it to find the final speed of separation. The final answer reflects the interaction of both masses and their respective velocities.
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Homework Statement



Outside the International Space Station, a 60 kg astronaut holding a 4.0 kg object (both initially at rest) throws the object at 10 m/s relative to the space station. A 50 kg astronaut, initially at rest, catches the object. What is the speed of separation of the two astronauts?

Homework Equations



p = mv
FΔt = Δp

Law of Cons. of Momentum
Pi = Pf

The Attempt at a Solution



Pi = Pf
(4)(10) = (50)(v)
v = 0.8 m/s

which is wrong :( not sure how to approach this question, any help please? thank you!
 
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When the astronaut throws the with some velocity, he will recoil. Find the velocity of recoil v of the first astronaut.
For second astronaut,
m1v1 = (m1 + m2)v2.
where m1 is the mass of the object and v1 its velocity. m2 is the mass of the second astronaut and v2 is the combined velocity.
finally the velocity of separation is (v+v2)
 

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