Let's break down the problem: ### Given Data - Mass of ball A, \(m_1 = 5\, \text{kg}\) - Velocity of A, \(u_1 = 10\, \text{m/s}\) (right) - Mass of ball B, \(m_2 = 10\, \text{kg}\) - Velocity of B, \(u_2 = -4\, \text{m/s}\) (left, so negative) - Coefficient of restitution, \(e = .6\) We are to find the velocities immediately after impact: \(v_1\) (A) and \(v_2\) (B). --- ## Step 1: Conservation of Momentum \[ m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2 \] \[ 5 \times 10 + 10 \times (-4) = 5v_1 + 10v_2 \] \[ 50 - 40 = 5v_1 + 10v_2 \] \[ 10 = 5v_1 + 10v_2 \] \[ 1 = .5v_1 + v_2 \tag{1} \] --- ## Step 2: Coefficient of Restitution \[ e = \frac{v_2 - v_1}{u_1 - u_2} \] \[ .6 = \frac{v_2 - v_1}{10 - (-4)} \] \[ .6 = \frac{v_2 - v_1}{14} \] \[ v_2 - v_1 = 8.4 \tag{2} \] --- ## Step 3: Solve the Two Equations From (1): \(1 = .5v_1 + v_2\) From (2): \(v_2 - v_1 = 8.4\) Solve for \(v_1\) and \(v_2\): From (2): \(v_2 = v_1 + 8.4\) Plug into (1): \[ 1 = .5v_1 + (v_1 + 8.4) \] \[ 1 = 1.5v_1 + 8.4 \] \[ 1 - 8.4 = 1.5v_1 \] \[ -7.4 = 1.5v_1 \] \[ v_1 = -4.93\, \text{m/s} \] Now, \(v_2 = v_1 + 8.4 = -4.93 + 8.4 = 3.47\, \text{m/s}\) --- ## Step 4: Final Answers \[ \boxed{v_1 = -4.93\, \text{m/s}, \quad v_2 = 3.47\, \text{m/s}} \] --- ## Correct Option Based on the options in the image: - Option at line 11: **3.47 m/s and -4.93 m/s** So the correct answer is: ### **3.47 m/s and -4.93 m/s** (Option at line 11)