A woman stands in the middle of a perfectly smooth, frictionless,frozen lake. She can set herself in motion by throwing things, but suppose she has nothing to throw. Can she propel herself to shore without throwing anything?

An internal force is a force exerted by one part of a system on another.

An external force is a force exerted on any part of a system by something outside the system.

If the net external force on a system is zero, the total momentum of the system $\overrightarrow{\mathbf{P}}$(the vector sum of the momenta of the individual particles that make up the system) is constant or conserved. Each component of total momentum is separately conserved.

$\overrightarrow{\mathbf{P}}\mathbf{=}\overrightarrow{{\mathbf{P}}_{\mathbf{A}}}\mathbf{+}\overrightarrow{{\mathbf{P}}_{\mathbf{B}}}$

If the net force is zero.

$\mathbf{\sum }_{\mathbf{}}\overrightarrow{\mathbf{F}}\mathbf{=}\mathbf{0}$

Then, the momentum is,

$\overrightarrow{\mathbf{P}}\mathbf{=}\mathit{c}\mathit{o}\mathit{n}\mathit{s}\mathit{t}\mathit{a}\mathit{n}\mathit{t}$

From the conservation of momentum, she can set herself in motion by blowing the air from her mouth.

Therefore, she can propel herself to shore without throwing anything. If she inhales the air vertically and blows that air in the horizontal direction, she can move in the horizontal direction thus she can propel herself to shore.