An air-track glider undergoes a perfectly inelastic collision with an identical glider that is initially at rest. what fraction of the first glider's initial kinetic energy is transformed into thermal energy in this collision?

Refer to the diagram shown below.

The initial KE (kinetic energy) of the system is
KE₁ = (1/2)mu²

After an inelastic collision, the two masses stick together.
Conservation of momentum requires that
m*u = 2m*v
Therefore
v = u/2

The final KE is
KE₂ = (1/2)(2m)v²
       = m(u/2)²
       = (1/4)mu²
      = (1/2) KE₁

The loss in KE is
KE₁ - KE₂ = (1/2) KE₁.

Conservation of energy requires that the loss in KE be accounted for as thermal energy.

  1/2