A2.90-kg ball, moving to the right at a velocity of 4.69 m/s on a frictionless table, collides head-on with a stationary 8.80-kg ball. find the final velocities of (a) the 2.90-kg ball and of (b) the 8.80-kg ball if the collision is elastic. (c) find the magnitude and direction of the final velocity of the two balls if the collision is completely inelastic.

Elastic collision:
momentum initial = momentum final
Kinetic energy is conserved

2.90-kg ball,
Since kinetic energy is conserved, velocity transferred to other ball so final velocity is v₁ = 0 m/s

8.80 kg ball
Since kinetic energy is conserved, velocity transferred to this ball so final velocity is v₂ = 4.69 m/s right

For perfectly inelastic, masses are combined and they stick together. One final velocity, v

m₁ = 2.90 kg
v₁ᵢ = 4.69 m/s right

m₂ = 8.80 kg
v₂ᵢ = 0 m/s

v = ? m/s

Momentum is conserved

m₁v₁ᵢ + m₂v₂ᵢ = v(m₁ + m₂)

v = (m₁v₁ᵢ + m₂v₂) / (m₁ + m₂)
v = (2.90 kg * 4.69 m/s + 0) / (2.90 kg + 8.80 kg)
v = 1.16 m/s