Final answer:
The problem is a physics question that requires the application of the conservation of momentum and energy to find the velocities of two colliding blocks connected by a spring. However, without additional details on the type of collision or the spring's behavior, the final velocities cannot be determined.
Step-by-step explanation:
The question involves a collision between two blocks connected by a spring, and determining their velocities after the collision on a frictionless surface. This scenario falls under the conservation of momentum and the conservation of energy in Physics, particularly in the topic of collisions.
In the scenario provided, two blocks with masses m1 = 1.60 kg and m2 = 2.10 kg collide, with m1 moving to the right at 4.00 m/s and m2 moving to the left at 2.50 m/s. They are connected by a light spring with a spring constant of 600 N/m. To determine their velocities after the collision, one must apply the principles of both conservation of momentum and conservation of mechanical energy, since the spring introduces potential energy into the system during compression and decompression.
The initial momentum of the system can be calculated by summing the product of mass and velocity for each block. Similarly, the mechanical energy before the collision can be calculated by adding the kinetic energies of each block. After the collision, these quantities must be conserved, which allows us to set up equations and solve for the final velocities.
However, the final answer will also depend on the type of collision - elastic or inelastic. An elastic collision conserves kinetic energy, and each block would have an individual velocity after the collision. In an inelastic collision, kinetic energy is not conserved and sometimes the blocks stick together. This is not explicitly stated, so additional information may be necessary to give a complete answer.
It's important to note that the spring constant value and the properties of the spring are critical to solving this problem completely. Without these details or further understanding of the type of collision, we cannot provide the velocities of the blocks after the collision