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A spacecraft of mass \(m1\) with speed \(v_{1i} = 3v_s\), approaches Saturn which is moving in the opposite direction with speed \(v_s\). After interacting gravitationally with Saturn, the spacecraft swings around Saturn and heads off in the opposite direction from its approach direction. The mass of Saturn is \(m_s\), is much much larger than the mass of the spacecraft. Find the final speed, \(v_{1f}\), of the spacecraft after it is far enough away from Saturn to be nearly free of the gravitational pull of Saturn.
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