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 = 7.30 kg) and blocks L and R (each of mass m = 2.70 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 = 0.50 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 = 3.00 s, what are (a) the velocity of block C (including sign) and (b) the position of its center?

Explanation / Answer

velocity of block L = (v1 -3.2)i

momentum conservation

mL(v1-3.2) + (mc+mr)v1 = 0

v1 = 3.2mL/(mL+mc+mr)

v1 = 0.68 m/s

at t = 0.50 s

mc*v2 + mr(v2+3.2) = (mc+mr)v1

7.3v2 + 2.7v2 + 8.64 = 6.8

v2 = -0.184 m/s

part b )

betweem t = 0 and t = 0.5 s block moves = 0.34 m

between 0.5 and t = 3 s it moves

v2dt = -0.46 m

net displacement = -0.12 m

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