how could a person who is at rest on a completely frictionless ice covering pond reach the shore?could she do this by walking,rolling,swinging her arms ,or kicking her feet?how could a person be placed in a such position in the first place?
Let me start with your last question: how could a person be placed in a such position in the first place?
Yes, that would be difficult. My first thought involved a helicopter. And it would be difficult to accomplish depositing her with perfectly zero velocity toward the shore. But we are to assume it was accomplished. Perhaps she was rigged with ropes and she was pulled out there by someone one on the east shore and someone else on the west shore pulled on a second rope to stop her when she got to the center. And then she would have to disconnect herself from the ropes and let them be pulled off the ice, leaving her there. Mighty cooperative of her. All in the interest of science.
could she do this by walking,rolling,swinging her arms ,or kicking her feet?
Walking or rolling or kicking would not generate even a small velocity. She has zero velocity to begin with so acceleration would be required to develop a velocity - and acceleration requires a force. But there is nothing solid to push against. But swinging her arms is a possibility. Perhaps by swinging them in a motion like swimming, she could swim through the air. If she pushed the air around her in one direction, Newton's 3rd Law says there would be a force in the opposite direction. If she achieved even a small velocity, that velocity would carry her to the shore - because there is no friction. The swimming motion would have to be similar to the motion of someone swimming while submerged.
how could a person who is at rest on a completely frictionless ice covering pond reach the shore?
My answers here will be other possibilities I have thought of. The question does not say that wind is totally non-existent. Just standing in a light breeze would give her a small velocity. (I am a sailor.) Since it must be cold, I expect she is wearing a coat. She could throw the coat in one direction. By the principle of Conservation of Momentum, this would give her a small velocity in the opposite direction. The question does not declare that she has nothing that could be used as a tool. Maybe she just happened to have a shovel with her. She could chip the ice and push against the edge she created to create a velocity. Or even use a fingernail file. Or just throw the shovel or file. She could turn her head to the right to inhale and then turn her head left and blow. I think that's enough.
I hope this helps,