Answer:
v₃ = 1.625 [m/s]
Step-by-step explanation:
To solve this problem we must use the definition of linear momentum conservation, which tells us that momentum is conserved before and after a collision.
Since the collision is inelastic, the two bodies are joined after the collision.
P = m*v [kg*m/s]
m = mass [kg]
v = velocity [m/s]
where:
P = lineal momentum [kg*m/s]
Now, it is important to clarify that in the following equation we will take the left side of the equation as the momentum before the collision and the right side of the equal sign as the momentum after the collision.
Pbefore = Pafter
(m₁*v₁) + (m₂*v₂) = (m₁+m₂)*v₃
where:
m₁ = mass one = 5 [kg]
v₁ = velocity of the mass one = 2 [m/s]
m₂ = mass two = 3 [kg]
v₂ = velocity of the mass two = 1 [m/s]
v₃ = velocity of the combined masses after the collision [m/s]
Now replacing we have:
(5*2) + (3*1) = (5 + 3)*v₃
10 + 3 = 8*v₃
v₃ = 13/8
v₃ = 1.625 [m/s]