The question states: A railroad diesel engine weighs fourtimes as much as a frei

Question

The question states:

A railroad diesel engine weighs fourtimes as much as a freight car. If the diesel engine coasts at 5km/h into a freight car that is initially at rest, show that thespeed of the coupled cars is 4 km/h.

The answer provided makes sense,somewhat, but I am still slightly confused with how the person gotfrom 4m x 5 km/h + m x 0 = (4m+m)v with the final answerbeing 5km/h. How does the formula cancel out to give you thoseunits - considering we were never given an actual mass to workwith. More explanation would be helpful. Thanks

Explanation / Answer

Let the mass of the frieght car be.. m. So, mass of rail road engine is 4 times m = 4m Now, initially, speed of rail road diesel engine = 5 Km/h and that of frieght car = 0 Km/h After the collision , both cars are moving together.. Let theirspeed be v Km/h Applying Law of conservation of momentum, weget, 4m* 5 +m*0 = (4m+m)*v Solving the above equation gives. 20m =5m*v Hence, v=4km/h Thus Finally , the speed of the coupled cars is 4Km/h

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