This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values. We are given: Mass of the first ball, m_1 = 0.5 kg Initial velocity of the first ball, u_1 = 10 m/s Mass of the second ball, m_2 = 0.5 kg (since it has equal mass) Initial velocity of the second ball, u_2 = 0 m/s (at rest) The balls move off together, indicating a perfectly inelastic collision. We need to find their common final velocity, v. Step 2: Apply the principle of conservation of momentum. For a perfectly inelastic collision, the total momentum before the collision is equal to the total momentum after the collision. The formula is: m_1 u_1 + m_2 u_2 = (m_1 + m_2) v Step 3: Substitute the given values into the formula. (0.5 kg)(10 m/s) + (0.5 kg)(0 m/s) = (0.5 kg + 0.5 kg) v Step 4: Calculate the momentum before the collision. 5 kg · m/s + 0 kg · m/s = (1.0 kg) v 5 kg · m/s = (1.0 kg) v Step 5: Solve for the final velocity, v. v = 5 kg · m/s1.0 kg v = 5 m/s The final velocity with which they move off together is 5 m/s. Comparing this to the given options: A. 20 m/s B. 10 m/s C. 5 m/s D. 0.5 m/s The correct option is C. The final answer is C. 5 m/s.