Collision and Sliding - Conservation of Linear and Angular Momentum Consider a system that consists of a student (m - 70 kg) and a plank. The plank is uniform and narrow with a length 2b = 5 meters and a mass M - 50 kg. Initially, the plank is at rest on a frictionless horizontal M surface. The student runs towards the plank in a direction at right angles to its length with a velocity v = 3.0 m/'s, then jumps onto and sticks to the end as shown in the diagram. Preliminary Questions: i) Why is it valid to apply conservation of linear momentum, p. to the plank-student system? ii) Why is it valid to apply conservation of angular momentum, L, to the plank student system? a. Determine, Your, the center of mass of the plank-student system, at the instance of collision, relative to the student's location, at the instant of collision, in terms of b, m and M. Then solve numerically for this quantity. Treat the student as a point mass. b. Using the principle of conservation of linear momentum, determine the center of mass velocity, Van of the plank-student system after the collision in terms of v, m and M. Then solve for You numerically. c. Using the principle of conservation of angular momentum, determine the angular velocity, as, of the plank- student system about the matern center of muss after the collision in terms of m, M. b, you and v. (Important, if there is no physical hinge point in the system around which the system pivots, we must apply conservation of angular momentum through an as is about the system center of-masa). Then solve numerically for a