Two toy locomotives approach each other along the same line, and upon collision both stop dead still. One locomotive has three times the speed of the other and the sum of their masses is 4.48 kg.

Question

Two toy locomotives approach each other along the same line, and upon collision both stop dead still. One locomotive has three times the speed of the other and the sum of their masses is 4.48 kg. 
What is the mass of the faster locomotive?
What is the mass of the faster locomotive?

drwls · Accepted Answer

Since they come to a dead stop, they had equal and opposite momenta beforer the collision
Let M1 be the mass of the faster toy locomotive (speed V1) and M2 be mass of the slow the slow one (with speed V1/3).
M2 = 4.48 - M1
M2*V1/3 = M1*V1 = (4.48 -M1)*V1/3
V1 cancels out.
M1 = (4.48 -M1)/3
(4/3)M1 = 1.4933 kg
M1 = 1.12 kg
M2 = 3.36 kg