A man of mass m stands at the left end of a uniform plank of length L and mass M, which lies on a frictionaless surface of ice. If the man walks to the other end of the plank, then by what distance does the plank slide on the ice?

Explanation

To solve the problem of how far the plank slides on the ice when the man walks from one end to the other, we can use the principle of conservation of momentum and the concept of the center of mass. Here’s a step-by-step solution:

### Step 1: Understand the System
We have a man of mass \( m \) standing at one end of a plank of mass \( M \) and length \( L \) on a frictionless surface. When the man walks to the other end of the plank, the plank will slide in the opposite direction due to the conservation of momentum.

**Hint:** Consider the system as a whole and think about the forces acting on it.

### Step 2: Define the Displacements
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