Answer
0.85 of the original kinetic energy was lost in the collision.
Work Step by Step
Let $M$ be the mass of each car.
Original kinetic energy:
$KE_0 = \frac{1}{2}(M)(38 ~m/s)^2$
$KE_0 = 720M ~J$
Kinetic energy after the collision:
$KE_f = \frac{1}{2}(M)(15 ~m/s)^2$
$KE_f = 110M ~J$
The fraction of kinetic energy lost in the collision:
$\frac{720M - 110M}{720M} = 0.85$
Therefore, 0.85 of the original kinetic energy was lost in the collision.
