1. The problem statement, all variables and given/known data The figure shows a two-ended “rocket” that is initially stationary on a frictionless floor, with its center at the origin of an x axis. The rocket consists of a central block C (of mass M = 6.40 kg) and blocks L and R (each of massm = 1.90 kg) on the left and right sides. Small explosions can shoot either of the side blocks away from block C and along the x axis. Here is the sequence: (1) At time t = 0, block L is shot to the left with a speed of 2.80 m/s relative to the velocity that the explosion gives the rest of the rocket. (2) Next, at time t = 0.90 s, block R is shot to the right with a speed of 2.80 m/s relative to the velocity that block C then has (after the second explosion). At t = 2.80 s, what are (a) the velocity of block C (including sign) and (b) the position of its center? 2. Relevant equations 3. The attempt at a solution Okay so first I need to find the velocity of the center and right blocks after the explosion at t=0 Mass of right block(relative velocity- velocity of center and right blocks)=combined mass of right and left blocks*velocity of right and left blocks 1.90kg(2.80m/s-v)=8.30kg* v=0.523 m/s Taking that velocity and multiplying by 0.9 seconds gives the position of the center of the center block at the time that the second explosion occurs 0.523m/s*0.9s= 0.4707m Next is to use the same method to find the velocity of the center block after the second explosion, I will skip the equation modeling as it is redundant and crude as I am unable to use notation. 1.90kg(2.80m/s-v)=6.40kg*v v=0.6410 m/s but in the negative x direction so v=-0.6410 m/s Now this is where I became uncertain. Is this velocity of -0.6410 m/s the new velocity of the center block and as it is a frictonless surface the answer to part a or should it be added the the original velocity of 0.523 m/s? v=-0.6410m/s or v=-0.6410m/s+0.523m/s=-0.1703m/s That would also affect part b as it would be 0.4707m+-0.6410(2.8-0.9)=-0.7472 m or 0.4707m+-0.703(2.8-0.9)=0.14713m The problem being that I entered both sets of solutions and both proved to be incorrect. What is wrong with my approach of using the conservation of momentum?