"Relative" is an important word. Block L of mass mL = 1.90 kg and block R of mass mR = 0.500 kg are held in place with a compressed spring between them. When the blocks are released, the spring sends them sliding across a frictionless floor. (The spring has negligible mass and falls to the floor after the blocks leave it.)

Question

(a) If the spring gives block L a release speed of 1.80 m/s relative to the floor, how far does block R travel in the next 0.800 s?
(b) If, instead, the spring gives block L a release speed of 1.80 m/s relative to the velocity that the spring gives block R, how far does block R travel in the next 0.800 s?

Momentum L has is equal to the momentum R has.

1.90*1.80=.500*veloictyR

Relative to each other, velocityLrelative=VelocityRrelative

Now to compute the distance here, obviously the relative distances are of no value....they equal each other. Here you have to convert to an absolute relative to floor velocity. AGain, use the principle that the center of gravity is constant, or, the momentums are equal.

1.9*1.8=.5*velocityR
velocityR = 6.84 m/s

d=v*time
d=(6.84)(.8)
d=5.472m ???