Answer:
[tex]v_{1} = v -\frac{v_{2}}{2}[/tex] , [tex]v_{2} = 2(v - v_{1})[/tex]
Explanation:
COMPLETE QUESTION: Let two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary. Now assume that the mass of object 1 is 2m, while the mass of object 2 remains m. If the collision is elastic, what are the final velocities v1 and v2 of objects 1 and 2?
A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision. The total momentum before collision equals total momentum after collision.
⇒ m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
From the question, two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary. Therefore, the formula correctly expressing the conservation of linear momentum between the two objects is;
mv = mv₁ + mv₂
Now assume that the mass of object 1 is 2m, while the mass of object 2 remains m.
2mv = 2mv₁ + mv₂
2mv = m (2v₁ + v₂)
2v = 2v₁ + v₂
[tex]v = \frac{2v_{1} + v_{2}}{2}[/tex]
[tex]v_{1} = v -\frac{v_{2}}{2}[/tex]
v₂ = 2v - 2v₁
v₂ = 2(v - v₁)
