A rocket of mass \(975\,\text{kg}\) is moving at a speed of \(5.8 \times 10^{3}\,\text{m/s}\) relative to Earth. Along the line of its motion a pre-planned explosion separates the rocket into two pieces of equal mass. The pieces move with a speed of \(2.2 \times 10^{3}\,\text{m/s}\) relative to each other.