Mechanics Ways To Solve

Question 1

Particle collides obliquely with a wall.
Given initial velocity, e and equation of wall (vector form)
Solve for final velocity

Answer 1

If wall is (xi + yj)
Then initial velocity can be split into:
a(xi +yj) + b(yi - xj)
Solve for a and b
Perpendicular component x e
Parallel component the same
Work out final velocity

Question 2

Solve for e when given final velocity and initial velocity (vector form)

Answer 2

Work out impulse in terms of m
As I = m(v - u)
Component of each velocity perpendicular to the wall given by dot product of velocity and impulse
e = u.I/v.I