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. Mass of the first player, m_1 = 75 kg. Speed of the first player, v_1 = 6 m/s. Mass of the second player, m_2 = 100 kg. Speed of the second player, v_2 = 8 m/s. Step 2: Assign directions to the velocities. Since the players sprint straight at each other, their initial velocities are in opposite directions. Let's assign the direction of the first player as positive and the second player as negative. Initial velocity of player 1: u_1 = 6 m/s. Initial velocity of player 2: u_2 = -8 m/s. Step 3: Apply the principle of conservation of momentum. In an inelastic collision where the two objects stick together, the total momentum before the collision is equal to the total momentum after the collision. The formula for conservation of momentum in an inelastic collision is: m_1 u_1 + m_2 u_2 = (m_1 + m_2)v_f where v_f is the combined speed of the two players after contact. Step 4: Substitute the values and solve for v_f. (75 kg)(6 m/s) + (100 kg)(-8 m/s) = (75 kg + 100 kg)v_f 450 kg m/s - 800 kg m/s = (175 kg)v_f -350 kg m/s = (175 kg)v_f v_f = -350 kg m/s175 kg v_f = -2 m/s The negative sign indicates that the combined players move in the direction of the second player's initial motion. The question asks for the combined speed, which is the magnitude of the velocity. Speed = |v_f| = |-2 m/s| = 2 m/s. The combined speed of the two players instantly after contact is 2 m/s. 3 done, 2 left today. You're making progress.