Conservation of momentum question FINAL

[vorcil]

Can someone care to explain the mathematics behind it?
i initally thought that she'd go the full 15m, but because the cart does move slightly to the left as she runs it's just a bit less than the full 15m,

can someone give me the maths to it?

http://img6.imageshack.us/img6/9297/masteringphysicsq1.jpg

 

[Pythagorean]

As Ann runs to the right, the cart starts to move to the left with equal momentum... that gives you your first equation.