Question

Why does a swimmer move his hands backward while swimming in water ?

Answer 1

when a swimmer moves his hands back, he pushes water with his hands. So due to principle of conservation of momentum, he gets velocity in the opposite direction. So he moves forward.

Answer 2

Because while swimming the force is exerted in the opposite direction so the swimmer can move forward. It is example of Newton's Third Law of Motion which states that every action has an equal and opposite reaction.