Bullet embedding in moving block: speed

A bullet of mass 20 g moves at 400 m/s. A block of mass 1.98 kg moves at 100 m/s in the same direction. The bullet embeds itself in the block and they move together. Find their common speed.

Step-by-step

1. m₁v₁ + m₂v₂ = (m₁ + m₂)v
   Momentum is conserved in the collision (no external horizontal force)
2. v = (0.02×400 + 1.98×100) ÷ (0.02+1.98) = 103
   Perfectly inelastic collision: the bodies share one speed afterwards

Why it works

In a perfectly inelastic collision momentum is conserved while kinetic energy is not. The total momentum before the collision equals the momentum of the combined mass afterwards.

Common mistakes

• Conserving kinetic energy, which only holds for elastic collisions.
• Adding 20 g to 1.98 kg without converting the grams to kilograms first.

Related

inelastic-collision projectile-motion n-phy-collision-inelastic-1