Elastic Collision – Two Dimension

Example (1): A 2 Kg body moving under the effect of the force, if the body at rest at ??=0 and ???=2?????+(3??2?1)?????,
1. What is the momentum and the kinetic energy of the body at 2??.
2. What is the work done by this force from ??=0 to ??=2??.

Example (2): consider a system of three particle: ??1=1???? is at ???1=???+???(????) and has velocity ???1=2???(??????), ??2=1???? is at ???2=???+???(????) and has velocity ???2=???(??????), ??3=1???? is at ???3=???(????) and has velocity ???2=???+???+???(??????)
1. Determine the velocity of the center of mass.
What is the total linear momentum of this system.


Example (3): An object of mass ??1=3????, moving with velocity ??1=13(????), collide head on with another object of mass ??2=7???? moves with initial velocity ??2=3(????). Given that the collision is elastic, what are the final velocities of the two objects?

Example (4): Two object slide over a frictionless horizontal surface. The first object mass ??1=5????, is propelled with speed ??14.5(????) toward the second object, mass ??2=2.5???? which is initially at rest. After the collision, both objects have velocities are direction ??=30° on either side of the original line of motion of the first object. Is the collision elastic or inelastic?