The figure shows a two-ended \"rocket\" that is initiallystationary on a frictio

Question

The figure shows a two-ended "rocket" that is initiallystationary on a frictionless floor, with its center at the originof an x axis. The rocket consists of a central block C (of mass M =6.00kg) and blocks L and R (each of mass m=2.40kg) on the left andright sides. Small explosions can shoot either of the side blocksaway from block C and along the x axis. Here is the sequence: 1) attime t=0s, block L is shot tothe left with a speed of 3.80m/srelative to the velocity that the explosion gives the rest ofthe rocket. 2) Next, at time t=0.80s, block R is shot to the rightwith a speed of 3.80m/s relative to the velocity that block C thenhas. At t=0.280s, what are (a) the velocity of block C and (b) theposition of its center.

I am aware this type of question has already been asked but theprevious answer was not clear nor was it absolutely accurate Ibelieve.

Explanation / Answer

(a)     the velocity of block L in the frame ofreference indicated in the fig that goes with the problem is(v1 - 3) i^     the momentum conservation for the explosion at t= 0 gives that     mL (v1 - 3) +(mC + mR) v1 = 0     from which we get that     v1 = 3 mL / (mL+ mC + mR)         = ......... m / s     at t = 0.80 s momentum conservation for thesecond explosion gives that     mC v2 + mR(v2 + 3) = (mC + mR)v1                                    = ...... kg . m / s      after this solve for v2 (b)     between t = 0 and t = 0.80 s the block movesv1 t distance     between t = 0.80 and t = 2.80 s the block movesv2 t distance     the net displacement will be     x = v1 t - v2t        = ........ m

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