A particle of mass m kinetic energy K momentum p collides head on elastically with another particle of mass 2m at rest

Question

A) Momentum of first particle ?
B) momentum of second particle?
C) kinetic energy of first particle?
D) kinetic energy of second particle?

Answer 1

small letters for particle 1
capitals for particle 2

before
Particle 1
p = m v
K = .5 m v^2
Particle 2
p = 2 m* 0 = 0
K = (1/2)(2m) 0^2 = 0

after: va is particle 1 after, V is particle 2
p still = m v
but now m va + 2m V
K still .5 m v^2
but now .5m va^2 + .5 (2m)V^2
so
m v = m va + 2m V or v = va + 2V
so v^2 = va^2 + 4 va V + 4 V^2
and
v^2 = va^2 + 2 V^2
so
4 va V +4V^2 = 2 V^2
2va V = -V^2
V = -2va
va = -V/2
then
v= -V/2+ 2V
v = 3V/2
V = (2/3)v
va = -(1/3)v
take it from there

Answer 2

dont copy kid go do it youre self