simultaneous equations

[billq]

Hello, I am reading through a tutorial on collisions and came across a
problem used to find the final velocity of an object. The author used
conservation of momentum, conservation of kinetic energry and the
coefficient of restitution.
f = final
p1 + p2 = p1f + p2f
ke1 + ke2 = ke1f + ke2f
cof of restitution = e = (v2f - v1f) / (v1 - v2)
the author use simultanious eq to get

v1f = ( (e + 1) m2 v2 + v1(m1 - e m2) ) / (m1 + m2)
v2f = ( (e + 1) m1 v1 - v2(m1 - e m2) ) / (m1 + m2 )

I am having a difficult time figuring out how this happens. any help would
be appreciated
thanks
bill

[The TimeLord]

Post by billq
Hello, I am reading through a tutorial on collisions and came across a
problem used to find the final velocity of an object. The author used
conservation of momentum, conservation of kinetic energry and the
coefficient of restitution.
f = final
p1 + p2 = p1f + p2f

Conservation of momentum.

Post by billq
ke1 + ke2 = ke1f + ke2f

Conservation of energy (assuming no external forces which would result
in potential energy). Also assuming no heat loss.

Post by billq
cof of restitution = e = (v2f - v1f) / (v1 - v2)
the author use simultanious eq to get
v1f = ( (e + 1) m2 v2 + v1(m1 - e m2) ) / (m1 + m2)
v2f = ( (e + 1) m1 v1 - v2(m1 - e m2) ) / (m1 + m2 )
I am having a difficult time figuring out how this happens. any help
would be appreciated
thanks
bill

Definition of momentum is
p = m v

Definition of (kinetic) energy is
ke = 1/2 m v^2

So

m1 v1 + m2 v2 = m1 v1f + m2 v2f
m1 v1^2 + m2 v2^2 = m1 v1f^2 + m2 v2f^2 (multiplying by 2)

The rest follows by algebra.