The object at rest suddenly explodes into three parts with the mass ratio `2:1:1`. The parts of equal masses move at right angles to each other with equal speeds. What is the speed of the third part after the explosion?

Explanation

To solve the problem step by step, we will analyze the situation using the principles of conservation of momentum.

### Step 1: Define the Masses
Let the masses of the three parts be:
- Mass A (the largest part) = \(2m\)
- Mass B = \(m\)
- Mass C = \(m\)

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