Final answer:
The resulting speed of the two tangled cars is 2.5 m/s east.
Step-by-step explanation:
To find the resultant speed and direction of the two tangled cars, we need to apply the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision. Momentum is calculated by multiplying mass and velocity.
Before the collision:
Total momentum = (mass of car A * velocity of car A) + (mass of car B * velocity of car B)
Total momentum = (1500 kg * -15 m/s) + (2500 kg * 5 m/s)
Total momentum = -22500 kg·m/s + 12500 kg·m/s
Total momentum = -10000 kg·m/s
After the collision, the two cars stick together. So, the mass of the combined cars is the sum of the individual masses: 1500 kg + 2500 kg = 4000 kg.
To find the resultant velocity of the two tangled cars, we divide the total momentum after the collision by the mass of the combined cars:
Resultant velocity = Total momentum / mass of combined cars = -10000 kg·m/s / 4000 kg = -2.5 m/s
Since the direction of car A was west and the direction of car B was east, the resulting direction after the collision will be in the direction with the higher magnitude, which is east.
Therefore, the resulting speed of the two tangled cars is 2.5 m/s east. None of the given options (a, b, c, or d) correctly represent the resulting speed and direction.