Kinetic energy varies as a square of momentum. A rocket expoldes mid air. Its total momentum is conserved but its total kinetic energy increases. How is this possible?

Explanation

To understand how the kinetic energy of a rocket can increase while its total momentum remains conserved after an explosion, we can break down the explanation into several steps.

### Step-by-Step Solution:

1. **Understanding Kinetic Energy and Momentum**:
- Kinetic energy (KE) is given by the formula \( KE = \frac{1}{2} mv^2 \), where \( m \) is mass and \( v \) is velocity.
- Momentum (P) is defined as \( P = mv \).
- The relationship between kinetic energy and momentum can be expressed as \( KE \propto P^2 \). This means that kinetic energy is proportional to the square of momentum.
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