Two boys are sliding toward each other on a frictionless, ice covered skating rink. Jack, having mass 45.0 kg is gliding to the right at 8.00 m/s, and Ethan, mass 31.0 kg, is gliding to the left at 11.0 m/s along the same direction. When they collide nearly head-on, they grab each other and hang on.
(a) What is their translational velocity immediately thereafter?
(b) What fraction of their original kinetic energy is still mechanical energy after their collision?
(c) The boys decide to repeat the collision with the same original velocities, but this time moving along parallel lines 1.20 m apart. At closest approach, they lock arms and start rotating about their common center of mass. Given their masses, use the equation for the centre of mass to calculate where the centre of mass is for the two boys
(d) Model the boys as point particles and their arms as a massless cord that does not stretch. Find their angular speed about the centre of mass.