Help with clarifying steps for 1-Dimensional Collisions without known mass

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SUMMARY

The discussion focuses on solving a 1-Dimensional collision problem involving two vehicles: car A and truck B. Car A, moving at 20 m/s, collides with truck B, which has twice the mass of car A and is traveling in the opposite direction. After the collision, both vehicles move together at a final velocity of -6 m/s. The key equations used are the conservation of momentum (Pi = Pf) and the relationship m1v1 + m2v2 = (m1 + m2)Vf, which allows for the cancellation of mass terms in the calculations, leading to the final velocity of the truck being determined as 19 m/s.

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Homework Statement



I have a practice question in front of me, with the answer and the steps to reach it but I am having a tough go trying to figure out how to do the steps myself. Can someone please clarify the outlined area of the following question?

In a crash, test car A, was initially moving 20m/s, and Truck B, with twice the mass of car A, was traveling in the opposite direction, during a head on collision. The vehicles were stuck together after the collision, and the final velocity of the car was 6m/s in the opposite direction.

Homework Equations



Pi = Pf
m1v1 + m2v2 = (m1+m2)Vf

The Attempt at a Solution


m(20) + 2mV(truck initial) = (m + 2m)(-6)
20m + 2MVti = -18m
20m/s + 2Vti = -18m/s
V2 = 19m/s

Where my brain doesn't click is where the author has solved out the masses. If you have two sets of masses on the left side of the equation, and only one on the left, how can you just drop them all together?
Im sure this is probably some stupidly easy answer but when I go back to this type of question it doesn't solve out properly in my head.

Tips??
 
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m's will cancel out
20m-2mvt=-18m
(20-2vt) m=-18m
 
Last edited:

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