What is her velocity relative to the surface of the ice?

[Waveparticle]

Homework Statement

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 1.50m/s to the right relative to the plank.
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?

Homework Equations

m₁v_1i+m₂v_2i=m₁v_1f+m₂v_2f

The Attempt at a Solution

 

[zhermes]

That place where it says "the attempt at a solution," is where you attempt to solve the problem---or where you explain what you're having trouble with so that we can help you accordingly.

 

[Waveparticle]

The part I'm having trouble with is setting up the problem and plugging in the givens.

 

[zhermes]

Start out thinking about it conceptually. You're on a plank, which has zero friction with the surface its lying on. As you start to walk in one direction, what happens to the plank?

The equation you gave is just conservation of momentum: the initial total momentum of the system has to be equal to the final total momentum of the system. Say that $$m_1$$ is the girl, and $$m_2$$ is the plank, what are their initial velocities? What else can you plug in for in the equation? What's left?

 

[rwisz]

a) The girl's velocity relative to the surface of the ice can be calculated using the conservation of momentum equation, where m1 is the girl's mass and m2 is the plank's mass. Since the girl is walking at a constant velocity of 1.50m/s to the right relative to the plank, her initial velocity relative to the plank is also 1.50m/s to the right. This means that her final velocity relative to the plank is also 1.50m/s to the right. Therefore, her velocity relative to the surface of the ice is also 1.50m/s to the right.

b) The velocity of the plank relative to the surface of the ice can also be calculated using the conservation of momentum equation. Since the plank was originally at rest, its initial velocity relative to the surface of the ice is 0m/s. Using the same reasoning as in part a), the plank's final velocity relative to the surface of the ice is also 1.50m/s to the right. Therefore, the velocity of the plank relative to the surface of the ice is 1.50m/s to the right.