A bullet of mass 10g is fired into a block of wodd of 390g lying on smooth surface. The wooden block along with bullet now moves with velocity of 10ms . What was velocity of bullet

To find the initial velocity of the bullet before it was fired into the wooden block, we can use the principle of conservation of momentum. This principle states that the total momentum of a closed system remains constant if no external forces act on it. In this case, the bullet and the block form a closed system.

Understanding Momentum

Momentum is defined as the product of an object's mass and its velocity. Mathematically, it can be expressed as:

Momentum (p) = Mass (m) × Velocity (v)

Setting Up the Problem

Let's denote the following variables:

• m_b = mass of the bullet = 10 g = 0.01 kg (converted to kilograms)
• m_w = mass of the wooden block = 390 g = 0.39 kg (converted to kilograms)
• v_b = initial velocity of the bullet (what we want to find)
• v_w = initial velocity of the wooden block = 0 m/s (since it is at rest)
• v_f = final velocity of the block and bullet together = 10 m/s

Applying Conservation of Momentum

According to the conservation of momentum, the total momentum before the collision equals the total momentum after the collision. This can be expressed as:

m_b × v_b + m_w × v_w = (m_b + m_w) × v_f

Plugging in the Values

Since the wooden block is initially at rest, its momentum is zero:

0.01 kg × v_b + 0.39 kg × 0 = (0.01 kg + 0.39 kg) × 10 m/s

This simplifies to:

0.01 kg × v_b = 0.40 kg × 10 m/s

0.01 kg × v_b = 4 kg·m/s

Solving for the Bullet's Velocity

Now, we can solve for v_b:

v_b = 4 kg·m/s / 0.01 kg

v_b = 400 m/s

Final Thoughts

The initial velocity of the bullet before it struck the wooden block was 400 m/s. This example illustrates how momentum is conserved in a collision, allowing us to determine unknown velocities when masses and final velocities are known.