1. Understand the Concept
The principle of conservation of linear momentum states that the total momentum of a closed system remains constant. In simpler terms, in a collision, the total momentum before the collision equals the total momentum after the collision.
2. Define Variables
* m1: Mass of the car (1000 kg)
* v1: Initial velocity of the car (25 miles per second east)
* m2: Mass of the van (1500 kg)
* v2: Initial velocity of the van (0 m/s)
* vf: Final velocity of the car and van after the collision (what we want to find)
3. Convert Units
We need consistent units. Let's convert miles per second to meters per second:
* 1 mile = 1609.34 meters
* 25 miles/second = 25 * 1609.34 m/s ≈ 40233.5 m/s
4. Apply Conservation of Momentum
* Momentum before collision = Momentum after collision
* (m1 * v1) + (m2 * v2) = (m1 + m2) * vf
5. Solve for the Final Velocity (vf)
* (1000 kg * 40233.5 m/s) + (1500 kg * 0 m/s) = (1000 kg + 1500 kg) * vf
* 40233500 kg*m/s = 2500 kg * vf
* vf = 40233500 kg*m/s / 2500 kg
* vf ≈ 16093.4 m/s
Important Note: This answer is physically unrealistic. The calculated final velocity is much higher than the speed of sound, which is impossible in a typical collision. This highlights the importance of considering the following:
* Inelastic Collisions: Real-world collisions are rarely perfectly elastic. Some energy is lost as heat, sound, and deformation of the vehicles. This means the final velocity will be lower than calculated.
* Realistic Velocities: It's highly unlikely for a car to be traveling at 25 miles per second (40233.5 m/s).
To make this problem more realistic, use a much lower initial velocity for the car.
