Final answer:
When two individuals with the same mass throw objects of different masses at the same velocity, the recoil velocities will be the same due to the conservation of momentum, so both individuals will gain the same velocity as a result. Therefore, the correct option is c).
Step-by-step explanation:
When two people with the same mass throw two objects at the same velocity, and the first object is heavier than the second, we must consider the law of conservation of momentum to compare the recoil velocities of the people. According to this law, the total momentum of an isolated system remains constant if no external forces act upon it. Throwing an object is an example of an action-reaction pair as described by Newton's third law of motion, meaning the momentum gained by the object is equal and opposite to the momentum gained by the person throwing it.
Since momentum (p) is the product of mass (m) and velocity (v), p = m × v, for both people and objects to have the same momentum, and given that both people have the same mass, the recoil velocities must indeed be the same to conserve momentum. This is regardless of the difference in mass of the two objects thrown, provided the velocity at which they're thrown is identical. Therefore, the correct option is: c) Both people have the same velocity. This principle can be seen in various situations, such as firearms discharge (recoil of guns) or in space, where astronauts use tools and the recoil from the expelled object propels them in the opposite direction.