Question

two balls undergo a perfectly elastic collision. ball B has a mass twice that of ball A. find the velocities of both balls after the collision.
Velocity ball A=10.0m/s
Velocity ball B= -5.00m/s

Answer 1

1 = A, 2 = B ' means after collision m2 = 2 m1 = 2m

perfectly elastic means momentum and kinetic energy conserved.

assume collision is along x-axis as is rebound

m1 v1 + m2 v2 = m1 v1' + m2 v2' momentu

10 m1 - (2)(5) m1 = m1 v1' + 2 m1 v2'
10 m1 - (2)(5) m1 =0
m1 v1' + 2 m1 v2' =0
v1' = -2 v2'

(1/2) m1 v1^2 + (1/2) m2 v2^2 = (1/2) m1 v1'^2 + (1/2) m2 v2'^2 kinetic energy
m1 v1^2 + 2m1 v2^2 = m1 v1'^2 + 2m1 v2'^2 got rid of (1/2) and used m2=2m1
also use v1' = -2 v2'

10^2 + 2 (5)^2 = 4 v2'^2 +2 v2'^2
150 = 6 v2'^2

v2' = 5 m/s
v1' = -10 m/s

That's the method. Might need to check my math.