Final answer:
The collision scenario involves conservation of momentum to calculate the final velocity after an inelastic collision. Final velocity is obtained by vector addition of each car's momentum, and kinetic energy loss is found by calculating the initial and final kinetic energies and finding the difference.
Step-by-step explanation:
The scenario described involves a physics concept known as conservation of momentum in an inelastic collision, where two cars stick together after colliding. To calculate the final velocity of the cars after the collision, we must first calculate the momentum of each car before the collision and then use the law of conservation of momentum to find the combined final velocity of the two cars. Kinetic energy loss can be found by calculating the initial and final kinetic energies and taking the difference.
(a) To find the final velocity (magnitude and direction), we determine the total momentum for each direction (south for the first car and west for the second car). Using these values, we can calculate the final velocity vector using vector addition.
For the first car (mass = 1200 kg, velocity = 8.00 m/s south), the momentum is p1 = mass × velocity = 1200 kg × 8.00 m/s = 9600 kg·m/s southwards.
For the second car (mass = 850 kg, velocity = 17.0 m/s west), the momentum is p2 = mass × velocity = 850 kg × 17.0 m/s = 14450 kg·m/s westwards. Using vector addition, the resultant momentum vector can be found which gives us the direction and magnitude of the final combined velocity.
(b) The kinetic energy lost is the difference between the initial kinetic energies of both cars and the kinetic energy after the collision. The initial kinetic energies are 0.5 × mass × velocity^2 for each car. The final kinetic energy is 0.5 × total mass × final velocity^2. Subtracting the final kinetic energy from the sum of the initial kinetic energies gives us the kinetic energy lost.