A 3 kg ball moving to the right at 4 m/sec collides with a 4 kg ball moving to the right at 2 m/sec. Find the final velocities of the balls in m/sec if the coefficient of restitution is 0.6. A. 2.2, 3.4
B. 1, 2
C. 4, 5
D. 6, 8

Option A

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

We have the value of one final velocity, let's see the other one.

V₄ = 1.2 + V₃

V₄ = 1.2 + 2.17

The closest values to these results are in option A, so this will be the correct option.

Hope this helps

answer: 31, 5556. 952 seconds