Answer
$3.8\times 10^7 ~J$ of thermal energy is produced in the collision.
Work Step by Step
After the collision, there is no kinetic energy in the system. All of the original kinetic energy of the trains is transformed into thermal energy. Therefore,
$v = (85 ~\frac{km}{h})(\frac{1000 ~m}{1 ~km})(\frac{1 ~h}{3600 ~s})$
$v = 24 ~m/s$
Next, we find KE which is equal to the thermal energy produced:
$KE = 2\times \frac{1}{2}mv^2$
$KE = (66,000 ~kg)(24 ~m/s)^2$
$KE = 3.8\times 10^7 ~J$
$3.8\times 10^7 ~J$ of thermal energy is produced in the collision.
