A 1000 kg car moving a 10 m/s collides with a stationary 2000 kg truck. The two vehicles interlock as a result of the collision. What is the final velocity of the two combined vehicles?
To find the final velocity of the two combined vehicles after the collision, we can use the principle of conservation of momentum.
Momentum is defined as the product of mass and velocity. According to the principle of conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision.
Before the collision, we need to calculate the momentum of both the car and the truck separately.
The momentum of an object is given by the equation:
Momentum = mass * velocity
For the car:
Momentum of the car before the collision = mass of the car * velocity of the car
= 1000 kg * 10 m/s
= 10,000 kg·m/s
For the truck:
Momentum of the truck before the collision = mass of the truck * velocity of the truck
= 2000 kg * 0 m/s (since it's stationary)
= 0 kg·m/s
Now, let's consider the momentum of the combined vehicles after the collision. Since the vehicles interlock, they move as one unit.
Let V be the final velocity of the two combined vehicles after the collision. The total mass of the combined vehicles is the sum of the masses of the car and the truck. Therefore:
Total mass = mass of the car + mass of the truck
= 1000 kg + 2000 kg
= 3000 kg
Using the principle of conservation of momentum, we can write:
Momentum before the collision = Momentum after the collision
(10,000 kg·m/s) + (0 kg·m/s) = Total mass * V
Simplifying the equation:
10,000 kg·m/s = 3000 kg * V
Dividing both sides by 3000 kg:
V = 10,000 kg·m/s / 3000 kg
V ≈ 3.333 m/s
Therefore, the final velocity of the two combined vehicles after the collision is approximately 3.333 m/s.