Mr. Sharma ( 50 kg ) and Mr. Gupta ( 60 kg ) are seated at the two opposite ends of a 4 m long boat ( 40 kg ) resting still in water. In order to discuss a mechanics problem, they move to the middle of the boat. Neglecting friction with the water, determine how far the boat moves on the water during this process.

Step-by-step solution

Since there is no external force acting on the system in the horizontal direction, the center of mass of the system remains stationary. Let the initial position of the center of the boat be at the origin, x_B = 0 . The length of the boat is L = 4 m . Let Mr. Sharma ( m_S = 50 kg ) be at one end, x_S = -2 m , and Mr. Gupta ( m_G = 60 kg ) be at the other end, x_G = 2 m . The mass of the boat is m_B = 40 kg . The initial position of the center of mass of the system is: x_ cm = m_S x_S + m_G x_G + m_B x_B m_S + m_G +