Final answer:
In a rear-end collision between an 800 kg sports car and a 1200 kg truck, the final velocity of the two vehicles after the collision can be determined using conservation of momentum. By calculating the momentum of each vehicle before the collision and summing them, the total momentum after the collision can be found. Dividing the total momentum by the combined mass of the vehicles gives the final velocity of 20.2 m/s, indicating their forward movement together.
Step-by-step explanation:
In this scenario, we have a rear-end collision between an 800 kg sports car and a 1200 kg truck. To find the final velocity of the two vehicles after the collision, we need to apply the principles of conservation of momentum.
Before the collision, the momentum of the sports car is given by: momentum_sports_car = mass_sports_car x initial_velocity_sports_car = 800 kg x -13 m/s = -10400 kg·m/s (negative sign indicates opposite direction).
The momentum of the truck is given by: momentum_truck = mass_truck x initial_velocity_truck = 1200 kg x 25 m/s = 30000 kg·m/s.
Since momentum is conserved in a collision, the total momentum after the collision is equal to the sum of the momentum before the collision:
magnitude of momentum_after = |momentum_sports_car| + |momentum_truck| = 10400 kg·m/s + 30000 kg·m/s = 40400 kg·m/s.
The combined mass of the sports car and the truck is 800 kg + 1200 kg = 2000 kg. Therefore, the final velocity of the two vehicles after the rear-end collision is:
final_velocity = magnitude of momentum_after / combined_mass = 40400 kg·m/s / 2000 kg = 20.2 m/s.
The final velocity indicates that the two vehicles will move forward together at a speed of 20.2 m/s.