A 67 kg man stands at the front end of a uniform boat of mass 179 kg and of length, L = 2.5 m. Assume there is no friction or drag between the boat and water. (a) What is the location of the center of mass of the system when the origin of our coordinate system (i) on the man's original location (ii) on the back end of the boat? [4 marks]
(b) If the man walks from the front end to the back end of the boat, by how much is the boat displaced? [3 marks]
(c) Now consider the man and his friend with identical mass of 67 kg are rowing the boat on a hot summer afternoon when they decide to go for a swim. The man jumps off the front of the boat at speed 3 m/s and his friend jumps off the back at speed 4 m/s. If the boat was moving forward at 1.5 m/s when they jumped, what is the speed of the boat after their jump?