The figure shows a two-ended “rocket” that is initially stationary on a friction

Question

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 = 6.20 kg) and blocks L and R (each of mass m = 2.30 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 3.20 m/s relative to the velocity that the explosion gives the rest of the rocket. (2) Next, at time t = 0.80 s, block R is shot to the right with a speed of 3.20 m/s relative to the velocity that block C then has (after the second explosion). At t = 3.40 s, what are (a) the velocity of block C (including sign) and (b) the position of its center?

Explanation / Answer

1. when the block L is shot

2.30x3.20 = [6.20 +2.30] xV

Vcr = 0.865 m/s [ towards right]

2.

mcvc+mrvr =mcVc'+mrvr'

vcr(mc+mr) = mcVc'+mrvr'

0.865(8.5) = 6.20Vc'+ 2.30x3.20

7.3525 -7.36 = 6.20 Vc'

Vc' = -1.20x10^-3 m/s

3.)

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