Collisions in two dimensions

Collision in two dimensionsA passenger car and a pickup truck have collided. Their bumpers lock and the pair skid together across the pavement. Police, insurance agents, and lawyers will analyze the scene in hopes of determining who was at fault. They can determine the post-collision speed from the distance that the two vehicles slid. They also use the direction the vehicles moved after the collision to determine the relative momentum each vehicle had before the accident. The law of conservation of momentum tells the reconstruction team the relationship between the vehicles’ initial speeds and the distance the vehicles traveled after colliding. Read the text aloud
To determine the relative speeds of the vehicles before the collision, the team uses momentum conservation. Since momentum is a vector quantity, the total momentum along each axis must be considered separately. Read the text aloud
Steps to follow to analyze the result of a perfectly inelastic collision in two dimensions.
Let’s follow the procedure above for the car–truck collision. Multiply each vehicle’s mass and velocity to calculate its momentum. The car’s momentum is entirely along the x-axis, while the truck’s momentum is along the y-axis. We use the Pythagorean theorem to calculate the total momentum. Since the total momentum is conserved, we equate the total momentum before the collision to the final momentum of the vehicles afterward. We divide the final momentum by the total mass to calculate their mutual velocity after colliding. Read the text aloud Show Checking the kinetic energy
Step-by-step analysis of the illustrated car-truck crash.
Two identical passenger cars enter an intersection at right angles and collide. Car A enters from the west (left), and Car B enters from the south (below). They stick together and skid to the northeast, at a 45° angle to the street grid. Which statement describes their relative speeds prior to the collision?
  1. Car A was traveling faster than Car B.
  2. The cars were traveling equally fast.
  3. Car B was traveling faster than Car A.
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A 800 kg passenger car enters an intersection from the west (left) and collides with a northbound pickup truck (whose mass is twice that of the car). The vehicles stick together and skid to the northeast, at a 45° angle to the street grid. Which statement correctly describes their relative speeds prior to the collision?
  1. The car was traveling faster than the truck.
  2. The car and truck were traveling equally fast.
  3. The car was traveling more slowly than the truck.
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