A glowing blue mote of mass 32.3 g is traveling east at 4.50 m/s when it collides and merges with another mote of mass 78.0 g that is traveling west at 1.12 m/s. find the velocity of the motes after they merge together (be sure to include direction).

Conservation of momentum so the total initial momentum in the system is equal to the total final momentum in the system. You must remember that if an object is travelling in the negative direction, you must put a negative sign for the velocity.

mv + mv = mv

plug in all the numbers

(0.0323) (4.50) + (0.078) (-1.12) = (0.0323 + 0.078) Vf

multiply everything together

0.14535 - 0.08736 = 0.1103Vf

simplify

0.05799 = 0.1103Vf

isolate for vf

Vf = 0.5257m/s east