Really though relative motion/momentum question

[404]

Okay, really tough for me atleast.

A 45 kg girl is standing on a 150 kg plank. The plank, originally at rest, is free to slide on a frozen lake, which is a flat, frictionless surface. The girl begins to walk along the plank at a constant velocity of 1.5 m/s to the right relative to the plan. a) what is her velocity relative to the surface of the ice? B) What is the velocity of the plank relative to the surface of the ice?

Answers are 1.15 m/s and 0.346 m/s
edit: title = tough*

 

[HallsofIvy]

Conservation of momentum. Or that the center of mass of the girl-plank system must remain stationary since there is no outside force on the system.

Be careful with speeds. If the plank's speed, relative to the ice is v, then the girl's speed relative to the ice is (1.5+ v) m/s (of course, the plank moves opposite to the girl so v will be negative). The girl's momentum, then, is
45(1.5+ v) kgm/s and the plank's is 150 v kgm/s. By conservation of momentum, 45(1.5+ v)+ 150v= 0.

 

[404]

Got it... Thanks!