Suppose their common speed before separation is v,
Spacecraft 1's speed after separation is v1
Spacecraft 2's speed after separation is v2
Note that in this case, the momentum is conservative along both the x and y directions.
So
Along X axis: (m1 + m2)v = m1v1cos(5.10) + m2v2cos(5.90)...
Connect points T and R.
Connect points T and Q.
Quadrilateral HRTQ is a parallelogram because HM = MT and MR = MQ.
Thus
TR is perpendicular to PR, and
TQ is perpendicular to PQ.
Let N be the midpoint of PT.
Connect points N and R.
Connect points NQ.
In right triangle PRT, NR = PT/2.
In right...
An alternative solution
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