A bullet of mass `2 g` travelling at a speed of `500 m//s` is fired into a ballistic pendulum of mass `1.0 kg` suspended from a cord `1.0 m` long. The bullet penetrates the pendulum and emerges with a velocity of `100 m//s`. Through what vertical height will the pendulum rise?

Explanation

To solve the problem step by step, we will use the principles of conservation of momentum and energy.

### Step 1: Understand the Problem
We have a bullet of mass \( m_b = 2 \, \text{g} = 0.002 \, \text{kg} \) traveling at a speed of \( v_b = 500 \, \text{m/s} \). It penetrates a ballistic pendulum of mass \( m_p = 1.0 \, \text{kg} \) and emerges with a speed of \( v_b' = 100 \, \text{m/s} \). We need to find the height \( h \) to which the pendulum rises after the bullet passes through it.

### Step 2: Apply Conservation of Momentum
Before the collision, the momentum of the system is only due to the bullet since the pendulum is at rest.

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