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, we need to analyze the explosion of the object into three parts and apply the principle of conservation of momentum. Let's break down the steps:

### Step 1: Understand the mass distribution
The object explodes into three parts with mass ratios of \(2:1:1\). Let's denote the total mass of the object as \(4M\). Therefore, the masses of the three parts will be:
- Mass 1 (\(m_1\)) = \(2M\)
- Mass 2 (\(m_2\)) = \(M\)
- Mass 3 (\(m_3\)) = \(M\)

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