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 = 5.10 kg) and blocks L and R (each of mass m = 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 2.70 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 2.70 m/s relative to the velocity that block C then has (after the second explosion). At t = 2.50 s, what are (a) the velocity of block C (including sign) and (b) the position of its center?

Explanation / Answer

Let V1 be the velocity relative to the lab, of the GR combination after the first explosion. Then momentum conservation implies

1.9 (-2.7+V1) + (5.1+1.9) V1 = 0

-5.13 + 1.9V1 + 7V1 = 0

V1 = 0.576 m/s

Let V2 be the velocity of G after the second explosion. Again momentum conservation dictates that:

(5.1+1.9) V1 = 5.1 V2 + 1.9 (V2 + 2.7)

4.03 = 5.13 + 7 V2

(a) V2 = -0.157 m/s

(b) X = V1*0.9 s + V2 * (2.5s-0.9s)

= (0.576m/s * 0.9s) + (-0.157m/s * 1.6s)

= 0.2672 m

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