A spaceship of mass 2.0 × 10⁶ kg is cruising at a speed of 5.0 × 10⁶ m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.0 × 10⁵ kg, is blown straight backward with a speed of 2.0 × 10⁶ m/s. A second piece, with mass 8.0 × 10⁵ kg, continues forward at 1.0 × 10⁶ m/s.
What are the direction and speed of the third piece?