Question

Imagine two carts with different masses colliding (m₁ = 1.0 kg, m₂ = 2.0 kg). If cart one is initially moving at 10 m/s and the other cart is moving at -5.0 m/s, calculate the final speed of each mass after they have a 100% inelastic collision. Please show all work!

Answer 1

After 100 percent inelastic collision, the two colliding masses combine with each other and move as a single object (mass of this single object being the sum of the two colliding masses).
And so, by using the conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. And so, we get


This is the velocity of the combined object after the collision. And putting the given values,

we get the final velocity

  
So, the final velocity of the combined mass is zero.