A team comprised of three people must run single file and leap onto an initially stationary, perfectly symmetrical, box-like, 4.0m long, 240kg sled (with uniform density) on frictionless ice (they begin to run before they encounter the ice). Their masses are 78 kg, 84 kg and 55 kg; their velocities are 19 m/s, 18 m/s and 16 m/s respectively; when the lead person is 3.0 m from the rear sss of the sled, the spacing between each person is 2.0 m. (a) Determine the centre of mass (measured along the horizontal only) of the team/sled system when the lead person is 3.0 m from the rear of the sled.

(b) Determine the centre of mass of the team/sled system once all three team members have leapt onto the sled. (You may assume, once on board, the team members are equally spaced between the front and rear of the sled with one meter gaps between them.)

(c) Once the team is on board, the sled encounters a 30◦ incline above the horizontal for which the coefficient of kinetic friction is 0.313; what maximum displacement does the sled achieve measured along the surface of the incline?