A train with a mass of 200,000 kg manages to brake to a speed of 3 m/sec before colliding with a truck with a mass of 2,000 kg that is stuck on the track. What speed does the truck move away from the train.
To find the speed at which the truck moves away from the train after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The equation for momentum is:
Momentum = mass × velocity
Let's denote the velocity of the train before the collision as vT1, the velocity of the truck before the collision as vT2, the velocity of the train after the collision as vT3, and the velocity of the truck after the collision as vT4.
The total momentum before the collision is:
Total momentum before = (mass of train × velocity of train) + (mass of truck × velocity of truck)
= (200,000 kg × vT1) + (2,000 kg × vT2)
The total momentum after the collision is:
Total momentum after = (mass of train × velocity of train after) + (mass of truck × velocity of truck after)
= (200,000 kg × vT3) + (2,000 kg × vT4)
Since the train manages to brake to a speed of 3 m/sec before colliding with the truck, we can set vT3 to 3 m/sec. As for the velocity of the truck after the collision, which we are trying to find, we'll denote it as vT4.
According to the law of conservation of momentum, we have:
Total momentum before = Total momentum after
(200,000 kg × vT1) + (2,000 kg × vT2) = (200,000 kg × vT3) + (2,000 kg × vT4)
Now we can solve for vT4, the speed at which the truck moves away from the train after the collision.
Note: To solve this equation, we would need additional information about the velocities of the train and truck before the collision (vT1 and vT2). Without that information, it's not possible to provide a specific answer for the speed at which the truck moves away from the train.