Suppose that block m = .050kg, sometime after reaching the base of the incline, undergoes a completely inelastic collision with the stationary block m = .075kg. use the principle of conservation of linear momentum to determine the common speed of the blocks just after the collision. (carry the answer to one decimal place)

The conservation of linear momentum for inelastic collision is written as:

m₁v₁ + m₂v₂ = (m₁+m₂)v'
where
v' is the common velocity after collision

We know m₁ = 0.050 kg, m₂ = 0.075 kg and v₂ = 0 (stationary). We don't know v₁ and v'. To solve this the number of unknowns should be equal to the number of independent equations. Since we have 2 unknowns and 1 equation, this is unsolvable. Suppose v₁ = 5 m/s, then v' equals

(0.05 kg)(5 m/s) + (0.075 kg)(0) = (0.05 + 0.075 kg)(v')
Solving for v',
v' = 2 m/s