Answer:
Option A
Step-by-step explanation:
To solve this problem we need to apply the momentum conservation, and analyze the data.
For this problem, I will call the initial velocities as V₁ and V₂, while the final velocities will be V₃ and V₄.
According to the momentum principle, this states the following:
m₁V₁ + m₂V₂ = m₁V₃ + m₂V₄ (1)
From this equation we can write an expression in function of V₃ and V₄. We also know that coefficient of restitution is 0.6. Knowing this, we can write the expression that will help us to solve for the final velocities:
e = V₄ - V₃ / 2 (2)
With both expressions we can solve for the final velocities. Let's use (1) first and see what we can simplify first by replacing the given data:
(3*4) + (4*2) = 3V₃ + 4V₄
12 + 8 = 3V₃ + 4V₄
20 = 3V₃ + 4V₄ (3)
This is all we can do for now. Let's use (2) now:
0.6 = V₄ - V₃ / 2
1.2 = V₄ - V₃
V₄ = 1.2 + V₃ (4)
Now, we can replace (4) into (3), and then, solve for V₃:
20 = 3V₃ + 4(1.2 + V₃)
20 = 3V₃ + 4.8 + 4V₃
15.2 = 7V₃
V₃ = 15.2 / 7
V₃ = 2.17 m/s
We have the value of one final velocity, let's see the other one.
V₄ = 1.2 + V₃
V₄ = 1.2 + 2.17
V₄ = 3.37 m/s
The closest values to these results are in option A, so this will be the correct option.
Hope this helps