Final answer:
The problem requires applying the conservation of momentum to calculate the final speed of the entangled vehicles post-collision. Changes in velocity for each vehicle are found by taking the difference between final and initial velocities. The change in kinetic energy is determined by comparing the total kinetic energy before and after the collision.
Step-by-step explanation:
The question at hand involves a traffic collision scenario where a pickup truck and a compact car collide head-on and stick together. This is a classic example of a problem in physics that uses principles of conservation of momentum and kinetic energy.
Part A: Speed of the Entangled Vehicles After the Collision
To find the final speed of the entangled vehicles, conservation of momentum is applied:
Total momentum before collision = Total momentum after collision
(Mass of truck × velocity of truck) + (Mass of car × velocity of car) = (Total mass) × (Final speed)
(1.78 × 10³ kg × 14.0 m/s) + (8.95 × 10² kg × -14 m/s) = (1.78 × 10³ kg + 8.95 × 10² kg) × Final speed
By solving the equation, we find the final speed of the vehicles post-collision.
Part B: Changes in Velocity of Each Vehicle
The change in velocity (Δv) for each vehicle is the difference between their final and initial velocities. Since they're entangled after collision, they'll have the same final velocity.
Part C: Change in Kinetic Energy
To find the change in kinetic energy of the system, subtract the total kinetic energy after the collision from the total kinetic energy before the collision:
Change in kinetic energy = Kinetic energy before collision - Kinetic energy after collision
Kinetic energy is given by the formula ½ mass × velocity squared (½mv²).
We calculate this separately for both vehicles before the collision and together for their entangled mass after the collision at the final speed determined in part A.