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 = 7.70 kg) and blocks L and R (each of mass m = 1.10 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 3.10 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 3.10 m/s relative to the velocity that block C then has (after the second explosion). At t = 2.90 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

1.1 (-3.1+V1) + (7.7+1.1) V1 = 0

-3.41 + 1.1V1 + 8.8V1 = 0

V1 = 0.344 m/s

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

(7.7+1.1) V1 = 7.7 V2 + 1.1 (V2 + 3.1)

3.03 = 3.41 + 8.8 V2

(a) V2 = -0.0435 m/s

(b) X = V1*0.5 s + V2 * (2.9s-0.5s)

= (0.344m/s * 0.5s) + (-0.0435m/s * 2.4s)

= 0.0676 m

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