A body of mass 5 kg moving at 10 m/s collides with a stationary body of mass 3 kg. If they stick together, what is their common velocity?

**The reasoning** This is **conservation of momentum** in action. When objects stick together after collision, total momentum before equals total momentum after. **Before collision:** - Moving body: momentum = mass × velocity = 5 kg × 10 m/s = 50 kg·m/s - Stationary body: momentum = 3 kg × 0 m/s = 0 kg·m/s - **Total momentum = 50 kg·m/s** **After collision:** - Combined mass = 5 kg + 3 kg = 8 kg - They move together with common velocity *v* - Total momentum = 8v Since momentum is conserved: 50 = 8v v = 50/8 = **6.25 m/s** **Why the wrong options tempt you** **A) 5.0 m/s** — You might average the velocities (10 + 0)/2, but momentum depends on mass too, not just speed! **C) 7.5 m/s** — You used only the moving mass (50/5 + 3 = 50/8? No!). You forgot to add both masses. **D) 13.0 m/s** — You added velocities like 10 + 3. Velocity doesn't simply add; momentum does! **Quick takeaway** In sticky collisions, the heavier object "wins" more—here the 5 kg pulls the final velocity closer to its original 10 m/s than to zero. Always: **(m₁v₁ + m₂v₂)/(m₁ + m₂)**.