Four trains coupling - find speed of resulting train

AI Thread Summary
To find the speed of the resulting four-car train after coupling, apply the principle of conservation of momentum, assuming a perfectly elastic collision. The initial momentum is calculated by multiplying the mass of the three slower cars (4 m/s) by their velocity and adding it to the momentum of the faster car (6 m/s). After coupling, the total mass is the sum of the four cars, and the final speed can be determined by dividing the total initial momentum by this combined mass. The resulting speed of the four-car train will be a weighted average based on the initial speeds and masses of the individual cars. This approach ensures that momentum is conserved throughout the coupling process.
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Three identical train cars, coupled together, are rolling east at 4 m/s. A fourth car traveling east at 6 m/s catches up with the three and couples to make a four-car train. What is the speed of the four-car train?

I have no idea what to do. Please Help...thanks in advance :)
 
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Start by assuming a perfectly elastic collision(no energy loss in the collision). Since the collision is elastic you can assume conservation of momentum before and after the collision. What is the momentum before and after the collision?
 

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