Relative Velocities: What is the direction of the plank's movement on the ice?

[mandy9008]

Homework Statement

A 45.0 kg girl is standing on a 163 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 1.52 m/s relative to the plank.
(a) What is her velocity relative to the surface of ice?
(b) What is the velocity of the plank relative to the surface of ice?

Homework Equations

m1v1i + m2v2i = m1v1f + m2v2f

The Attempt at a Solution

a. (45.0 kg)(0 m/s) + (163 kg)(0 m/s) = (45.0 kg)(v1f) + (163 kg)(1.52 m/s)
v1f=5.51 m/s

 

[kuruman]

Good beginning, but you need to express the velocity of the girl relative to the ground, not relative to the plank when you conserve momentum.

 

[mandy9008]

so how would I go about doing that?

 

[kuruman]

Say the girl is moving left to right. In what direction is the plank moving?

 

[rwisz]

b. (45.0 kg)(1.52 m/s) + (163 kg)(0 m/s) = (45.0 kg)(v2f) + (163 kg)(v2f)
v2f=0.88 m/s

I would say that the direction of the plank's movement on the ice is in the same direction as the girl's movement, which is to the right. This is because the plank and the girl are on a frictionless surface, so there are no external forces acting on them in the horizontal direction. Therefore, the velocities of the girl and the plank are equal and in the same direction.