A fully dressed person is at rest in the middle of a pond on perfectly frictionless ice and must get to shore. How can this be accomplished? Assuming you've answered them in terms of momentum conservation, answer them also in terms of Newton's third law (or vice versa, if you answered already in terms of Newton's third law).

I'll explain it in both conservation of momentum and newtons third law.

Conservation of momentum : The total momentum of a closed system is always a constant

Newtons third law : An action has an equal and opposite reaction

Now if you're fully dressed on a frictionless pond at rest and you want to go to shore you have to make a sacrifice. Take off your clothes and throw them in the direction you DONT want to go. So the opposite side of the shore. In the case of conservation of momentum, the intial momentum is zero thus the total of the final momentum should be zero too. Pi = Pf. Once you throw your clothes away your clothes' momentum will be (Mc) (-Vc) and your momentum will be (M) (V) adding those two HAS to result in a zero because your initial momentum was zero.

Now explaining it in terms of Newtons third law, if you throw your clothes away with a force, the clothes will exert the same exact force on you. Since the ice is frictionless that force will cause you to accelerate. Now the acceleration depends on your mass and the force you exerted on the clothes.

Hope it makes sense!