Two friends, Ankit and Bharat, each weighing 40 kg, sit at a separation of d on a frictionless platform. Ankit rolls a 4 kg ball along the platform towards Bharat, who catches it. Bharat subsequently rolls the ball back to Ankit, who catches it. This back-and-forth motion of the ball between the two friends continues. The ball travels at a constant speed of 5 m/s relative to the platform. What is the maximum number o

Step-by-step solution

Let the mass of Ankit and Bharat be M = 40 kg, and the mass of the ball be m = 4 kg. The speed of the ball relative to the platform is constant at v = 5 m/s. Thus, the momentum of the ball is always p = mv = 4 5 = 20 kg m/s when moving towards Bharat, and -20 kg m/s when moving towards Ankit. Each time Bharat catches the ball, he absorbs 20 kg m/s of momentum. When he rolls it back, he imparts -20 kg m/s to the ball, gaining another 20 kg m/s. Thus, in each catch-and-throw cycle, Bharat's momentum increases by 40 k