SOLUTION: A 2kg object travelling at 1.0 m/s collides head-on with a 1.0 kg object initially at rest. Determine the velocity of each object after the impact if the collision is perfectly ela

The term "the collision is perfectly elastic" means that after the collision the masses remain the same 
and both the momentum law and conservation of mechanical energy law are held. 


If  and  are the velocities of the particles after the collision, then the momentum conservation equation is

    2 kg * 1 m/s + 1 kg * 0 m/s =  + ,

Left side is the momentum value BEFORE the collision; right side is that AFTER the collision.  In the short form

     +  = 2   (kilogram*meter/s).                 (1)



The mechanical energy conservation equation is

      +  =  + .

Left side is the kinetic energy value BEFORE the collision; right side is that AFTER the collision.  In the short form

      +  = 1   (kg*m^2/s^2, or joules).     (2)



Thus you need solve the system of two equation (1) and (2) to find the unknowns    and  .



For it, from equation (1), express  and substitute it into equation (2).


In this way, you can complete the solution on your own.