Final answer:
To find the speed of the three joined cars after the collision, we can use the conservation of momentum principle. By adding the momenta and dividing by the total mass, we find that the final velocity is 1.52 m/s.
Step-by-step explanation:
To solve this problem, we can use the conservation of momentum principle. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Before the collision, the single railroad car has a momentum of (mass x velocity) = (1.86 x 10^4 kg) x (2.80 m/s) = 5.208 x 10^4 kg·m/s.
The two railroad cars already joined together have a combined momentum of (mass x velocity) = (2 x 1.86 x 10^4 kg) x (1.40 m/s) = 3.276 x 10^4 kg·m/s, as they have the same mass as the single car and are moving at the same velocity.
To find the final velocity of the three joined cars, we can simply add the momenta together and divide by the total mass:
Final velocity = (Total momentum) / (Total mass)
=(5.208 x 10^4 kg·m/s + 3.276 x 10^4 kg·m/s) / (1.86 x 10^4 kg + 2 x 1.86 x 10^4 kg)
= 8.484 x 10^4 kg·m/s / (1.86 x 10^4 kg + 3.72 x 10^4 kg)
= 8.484 x 10^4 kg·m/s / 5.58 x 10^4 kg
= 1.52 m/s
Therefore, the speed of the three joined cars after the collision is 1.52 m/s.