Final answer:
The activation speed for Forward Collision Warning (FCW) systems varies, typically starting at around 8-10 km/h (5-6 mph). For collision-related questions, physics can provide answers using the conservation of momentum. To calculate the post-collision velocity, velocities must be converted to m/s, and momentum vectors must be combined using the Pythagorean theorem and trigonometry.
Step-by-step explanation:
The minimum speed a vehicle must be traveling for the Forward Collision Warning (FCW) system to work is not explicitly mentioned in the information provided. FCW systems use sensors and algorithms to detect potential collisions and alert drivers. The speed at which they become active can vary by manufacturer, but most systems begin to operate at speeds around 8-10 km/h (5-6 mph). However, for the question regarding the velocity of the combined wreckage after a collision between a small car and a truck, physics principles can be applied to determine the result. This involves using the conservation of momentum, which states that the total momentum before the collision must equal the total momentum after the collision.
To calculate the velocity of the combined wreckage, we'll use the conservation of momentum. For a two-dimensional collision like the one described, we'll consider the momentum in each direction independently. First, we convert the velocities from km/hr to m/s:
- Small car (eastward): 60 km/hr = 16.67 m/s
- Truck (northward): 40 km/hr = 11.11 m/s
The momentum before the collision for the car is m1v1 (1200 kg = 16.67 m/s), and for the truck, it's m2v2 (3000 kg = 11.11 m/s). To find the magnitude and direction of the combined wreckage's velocity, we calculate the resultant vector of these momentums using Pythagorean theorem and trigonometry.
The final answer will be a combination of both magnitudes and direction, reflecting the new velocity vector of the combined wreckage. However, it's important to remember that this is an idealized situation that assumes a perfectly inelastic collision with no energy loss and it assumes no other forces acting at the moment of collision.