A bullet of mass 5gm is fired horizontally into block of mass 1kg at rest on a horizontal surface and gets embedded in it. The combination moves 5m before coming to rest. If `mu_(k)=0.40`, what is the speed with which the bullet strikes the block ?

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Problem
We have a bullet of mass \( m_b = 5 \, \text{g} = 0.005 \, \text{kg} \) that is fired horizontally into a block of mass \( m_B = 1 \, \text{kg} \) at rest. After the bullet embeds itself in the block, they move together and come to rest after traveling a distance of \( d = 5 \, \text{m} \). The coefficient of kinetic friction between the block and the surface is \( \mu_k = 0.40 \). We need to find the speed \( v \) with which the bullet strikes the block.

### Step 2: Use Conservation of Momentum
When the bullet embeds itself in the block, we can apply the conservation of momentum:

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