Final answer:
The change in kinetic energy of the car is -44,000 J (or -44 kJ) in a perfectly inelastic collision with the truck.
Step-by-step explanation:
The change in kinetic energy of the car can be calculated using the principle of conservation of momentum for perfectly inelastic collisions. In a perfectly inelastic collision, the two objects stick together after the collision and move as one. The change in kinetic energy can be calculated using the equation: Change in kinetic energy = initial kinetic energy - final kinetic energy.
Initially, the car has a kinetic energy of 1/2 x mass x (speed)^2 = 1/2 x 1500 kg x (4 m/s)^2 = 12,000 J. After the collision, the car and the truck will move together as one object. The final kinetic energy of the combined objects is given by: 1/2 x (mass of car + mass of truck) x (final velocity)^2.
The final velocity of the combined objects can be calculated using the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. The total momentum before the collision is given by: momentum of car + momentum of truck = mass of car x velocity of car + mass of truck x velocity of truck.
Using the values given in the question, the total momentum before the collision is: 1500 kg x 4 m/s + 50000 kg x 1.80 m/s = 6,000 kg m/s + 90,000 kg m/s = 96,000 kg m/s.
Since the car and the truck move together as one object after the collision, the total momentum after the collision is: (mass of car + mass of truck) x final velocity = (1500 kg + 50000 kg) x final velocity.
Setting the total momentum before the collision equal to the total momentum after the collision, we can solve for the final velocity:
96,000 kg m/s = (1500 kg + 50000 kg) x final velocity
96,000 kg m/s = 51,500 kg x final velocity
final velocity = 1.864 m/s.
Finally, we can calculate the final kinetic energy of the combined objects:
1/2 x (1500 kg + 50000 kg) x (1.864 m/s)^2 = 56,000 J.
The change in kinetic energy of the car is: Change in kinetic energy = initial kinetic energy - final kinetic energy = 12,000 J - 56,000 J = -44,000 J.
Therefore, the change in kinetic energy of the car is -44,000 J, or -44 kJ.