Answer:
If a heavier person exerts the same jump force, the platform would not move the same distance. This is because the platform's movement depends on both the force exerted by the person and the mass of the person.
According to Newton's third law, for every action, there is an equal and opposite reaction. When a person jumps on a platform, they exert a force on the platform, and the platform exerts an equal and opposite force on the person.
The force exerted by the person is the same in both cases (assuming they exert the same jump force). However, the mass of the person affects the resulting acceleration and movement.
Using Newton's second law (F = ma), we can see that the acceleration of an object is inversely proportional to its mass when the force is constant. In other words, a heavier person would experience lower acceleration compared to a lighter person when the same force is applied.
Since the platform's movement depends on the acceleration of the person, the heavier person would cause less acceleration and consequently move a shorter distance compared to a lighter person exerting the same jump force.