Question

two balls are part of a game where they are projected toward each other and collide elastically. the first ball (\\(m_1 = 30\text{ kg}\\)) moves toward the second ball at \\(7\text{ m/s}\\) in the positive x direction. the second ball (\\(m_2 = 35\text{ kg}\\)) moves toward the first ball at \\(6\text{ m/s}\\).

question 1
what is the final velocity of the first ball in m/s?

question 2
what is the final velocity of the second ball in m/s?

Explanation:

Set up conservation equations

$$
LATEXBLOCK0
$$

Solve for the final velocity of the first ball

$$
LATEXBLOCK1
$$

Solve for the final velocity of the second ball

$$ v_{2f} = v_{1f} + 13 = -7 + 13 = 6\text{ m/s} $$

Answer:

Question 1

The final velocity of the first ball is <blank>-7</blank> m/s.

Question 2

The final velocity of the second ball is <blank>6</blank> m/s.