Final answer:
The new velocity of the two cars after they join up is 3.32 m/s. The change in kinetic energy is -10,006.88 J.
Step-by-step explanation:
To solve this problem, we can use the principle of conservation of momentum. The total momentum before the cars join up is equal to the total momentum after they join up.
To find the new velocity of the two cars after they join up, we can use the equation:
m1v1 + m2v2 = (m1 + m2)v
Substituting the given values, we get:
(15,500 kg)(3.85 m/s) + (12,850 kg)(1.75 m/s) = (15,500 kg + 12,850 kg)v
Solving for v, we find that the new velocity of the two cars after they join up is 3.32 m/s.
To find the change in kinetic energy, we can use the equation:
change in kinetic energy = 0.5(m1 + m2)(vf2 - vi2)
Substituting the given values, we get:
change in kinetic energy = 0.5(15,500 kg + 12,850 kg)(3.32 m/s - 3.85 m/s)
Solving for the change in kinetic energy, we find that it is -10,006.88 J.