Percentage of kinetic energy after an elastic collision

  • Thread starter clope023
  • Start date
1. The problem statement, all variables and given/known data

A stationary object with mass mb is struck head-on by an object with mass ma that is moving initially at speed v0.

If the collision is elastic, what percentage of the original energy does each object have after the collision?

KA2/K1 = ?

KB2/K1 = ?

2. Relevant equations

K1 = 1/2mav1a^2 + 1/2mbv1b^2

K2 = 1/2mav2a^2 + 1/2mbv2b^2

3. The attempt at a solution

K1/K2A = (1/2mav1a^2 + 1/2mbv1b^2)/(1/2mav2a^2)

= v1a^2/v2a^2 + mbv1b^2/mav2a^2

I'm not sure how to proceed from here and get a percentage.

any help is appreciated.
mbvo=mbv1+mav2(mv conserved)
mbvo^2= mbv1^2+mav2^2(KE conserved)
making use of these equations, find v1,v2 in terms of mass. and vo...
v0 = v1 + mav2/mb

v1 = v0 - mav2/mb

v2 = mbv0/ma - mbv1/ma

found the velocities, but I'm not sure how to proceed.

I'm not sure what to do with these values?

plug them into the kinetic energy equations and solve perhaps?

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