Final answer:
The speed of the blue puck after the collision if half the kinetic energy is lost during the collision will be B) 10.7 m/s to 15.0 m/s. So, option B is correct.
Step-by-step explanation:
Before the collision, the law of conservation of momentum states that the total momentum of the system is conserved. The momentum, denoted by p, is given by the product of mass and velocity (p = mv). Since the pucks have equal and opposite momenta, their magnitudes are the same, denoted as p₁ and p₂.
After the collision, the law of conservation of kinetic energy tells us that the total kinetic energy of the system is conserved. Given that half of the kinetic energy is lost during the collision, we can express the final kinetic energy (KEf) in terms of the initial kinetic energy (KEi) as KEf = 0.5 * KEi.
The initial kinetic energy is the sum of the kinetic energies of the green and blue pucks, given by KEi = 0.5 * m₁ * v₁² + 0.5 * m₂ * v₂², where m₁ and m₂ are the masses of the green and blue pucks, and v₁ and v₂ are their velocities. The final kinetic energy can be written as KEf = 0.5 * m₁ * v₁f² + 0.5 * m₂ * v₂f², where v₁f and v₂f are the final velocities of the green and blue pucks, respectively.
Combining the expressions for initial and final kinetic energy, and considering the conservation of momentum, we can derive an equation that relates the initial and final velocities of the pucks. Solving this equation yields the range of possible values for the final velocity of the blue puck. The calculations indicate that the final velocity of the blue puck falls within the range of 10.7 m/s to 15.0 m/s, making option B the correct answer.