A bullet of mass 20 g moving horizontally at a speed of 300 m/s is fired into a wooden block of mass 500 g suspended by a long string. The bullet crosses the block and emerges on the other side. If the centre of mass of the block rises through a height of 20.0 cm, find the speed of the bullet as it emerges from the block.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the problem
We have a bullet of mass \( m_1 = 20 \, \text{g} = 0.02 \, \text{kg} \) moving with an initial speed \( u_1 = 300 \, \text{m/s} \). It strikes a wooden block of mass \( m_2 = 500 \, \text{g} = 0.5 \, \text{kg} \) which is suspended and can move vertically. After the bullet passes through the block, the block rises to a height \( h = 20 \, \text{cm} = 0.2 \, \text{m} \). We need to find the speed of the bullet as it emerges from the block, denoted as \( v' \).

### Step 2: Calculate the initial velocity of the block after the bullet passes through
When the block rises to a height \( h \), we can use the principle of conservation of energy. The potential energy gained by the block is equal to the kinetic energy it had just after the bullet passed through.

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