Final answer:
When two objects collide and stick together, their momentum is conserved. Using the principle of conservation of momentum, we can find the final velocity and direction of the entangled vehicles. In this case, the post-collision direction of the two vehicles is measured 0 degrees north of east.
Step-by-step explanation:
When two objects collide and stick together, their momentum is conserved. In this case, we can use the principle of conservation of momentum to find the final velocity and direction of the entangled vehicles.
First, we determine the initial momentum of each vehicle:
- For the Ford Explorer: momentum = mass × velocity = 1950.0 kg × 31.0 m/s = 60450.0 kg·m/s.
- For the garbage truck: momentum = mass × velocity = 13020.0 kg × 8.3 m/s = 108066.0 kg·m/s.
Since the two vehicles move as a single object after the collision, their final momentum is equal to the sum of their initial momenta:
Total momentum = 60450.0 kg·m/s + 108066.0 kg·m/s = 168516.0 kg·m/s.
To determine the final direction of the entangled vehicles, we must find the angle measured north of east.
Using trigonometry, we can calculate this angle using the equation:
tan(θ) = final velocity north / final velocity east.
Since the final velocity is 8.3 m/s and only in the east direction, the angle will be 0 degrees north of east.