Consider a sled of mass \(M=10 \mathrm{~kg}\) and length \(L=1.0 \mathrm{~m}\) on which is placed a mass \(m=3 \mathrm{~kg}\) (considered point-like) that can slide without friction in the plane of the sled, as in Fig.8.14

. Initially, the system is stationary, the center of mass of the sled is at the origin of the reference frame, and the mass is at the right end of the sled, at a distance \(L / 2\) from the origin. Then a small explosive charge (placed between the mass and the sled) sets the system in motion.

1. If the relative velocity between the sled and the mass is \(v_{r}=10 \mathrm{~m} / \mathrm{s}\), calculate the velocity of the sled and the mass after the explosion.
2. At a later instant, the mass elastically impacts the left side of the sled. Calculate the velocities of mass and sled after the impact.
3. At the last instant, the mass impacts completely in elastically against the right side of the sled. Calculate the new velocities after the impact.

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