a) The velocity of the truck immediately after the collision is 11.11 m/s to the right. b) The change in kinetic energy of the car-truck system due to the collision can be calculated by subtracting the initial kinetic energy from the final kinetic energy. c) The collision can be determined to be elastic or inelastic by comparing the total kinetic energy before and after the collision.
a) To find the velocity of the truck immediately after the collision, we can use the principle of conservation of momentum. The momentum before the collision is equal to the momentum after the collision. The momentum of the car before the collision is given by the equation: mass of the car multiplied by the initial velocity of the car. The momentum of the truck before the collision is given by the equation: mass of the truck multiplied by the initial velocity of the truck.
Therefore, we have (mass of the car x initial velocity of the car) + (mass of the truck x initial velocity of the truck) = (mass of the car x final velocity of the car) + (mass of the truck x final velocity of the truck). Plugging in the given values, we have (1200 kg x 25 m/s) + (9000 kg x 20 m/s) = (1200 kg x 17.5 m/s) + (9000 kg x final velocity of the truck). Solving for the final velocity of the truck, we find that it is 11.11 m/s to the right.
b) To find the change in kinetic energy of the car-truck system due to the collision, we need to calculate the initial kinetic energy of the car and the truck and subtract it from the final kinetic energy of the car and the truck. The initial kinetic energy of the car is given by the equation: (1/2) x mass of the car x (initial velocity of the car).
The initial kinetic energy of the truck is given by the equation: (1/2) x mass of the truck x (initial velocity of the truck)². The final kinetic energy of the car is given by the equation: (1/2) x mass of the car x (final velocity of the car)². The final kinetic energy of the truck is given by the equation: (1/2) x mass of the truck x (final velocity of the truck)². Substituting the given values, we can calculate the change in kinetic energy.
c) To determine if this is an elastic collision, we need to consider the conservation of kinetic energy. In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. If the total kinetic energy is conserved, then the collision is elastic. If the total kinetic energy is not conserved, then the collision is inelastic. By calculating the change in kinetic energy in part b), we can determine if it is zero (indicating an elastic collision) or nonzero (indicating an inelastic collision).