A 5.0 kg object and a 10 kg object, both resting on a frictionless table, are connected by a massless compressed spring. The spring is released and the objects fly off in opposite directions. The 5.0 kg object has a velocity of 8.0 m/s to the left. What is the velocity of the 10 kg object?

 The net external force on the objects is zero and linear momentum is conserved as the spring delivers its energy to the two objects. Choose a coordinate system in which the +x direction is to the right. Let object 1 be the 5 kg object and object 2 the 10 kg object. Apply conservation of linear momentum, then solve for the velocity of interest.