velocity and acceleration

Newton’s Second Law of Motion
The relationship between an object’s mass m, its acceleration a, and the applied force F is
F = ma.
Acceleration and force are vectors (as indicated by their symbols being displayed in bold font); in this law the direction of the force vector is the same as the direction of the acceleration vector.
For any two bodies of masses m1 and m2, the force of gravity between the two bodies can be given by the equation:
where d is the distance between the two objects and G is the constant of universal gravitation.
Just as we have two distinguished unit vectors i and j corresponding to the Cartesian coordinate system, we can likewise define two distinguished unit vectors ur and u? corresponding to the polar coordinate system


? Particle 1 is moving at velocity v1i and particle 2 is at rest
? In the x-direction, the initial momentum is m1v1i
? In the y-direction, the initial momentum is 0
? After the collision, the momentum in the x-direction is m1v1f cos q + m2v2f cos f
? After the collision, the momentum in the y-direction is m1v1f sin q - m2v2f sin f