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 = 6.70 kg) and blocks L and R (each of mass m = 1.50 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 2.90 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 2.90 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?

The figure shows a two-ended ½rocket½ 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 = 6.70 kg) and blocks L and R (each of mass m = 1.50 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 2.90 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 2.90 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

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

1.5 (-2.9+V1) + 8.2 V1 = 0
V1 = 0.448 m/s

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

8.2 V1 = 6.7 V2 + 1.5 (V2 + 2.9)

4.8 = 6 + 8 V2
V2 = -0.082 m/s

X = V1*0.9 s + V2 * (3s-0.9s)
= 0.448m/s * 0.9s -0.082m/s * 2.7s
= 18.18 cm
= 0.1818 m

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