Randall D. Knight — Impulse and Momentum: Problem 80

A spaceship of mass \(2.0 \times 10^6 \text{ kg}\) is cruising at a speed of \(5.0 \times 10^6 \text{ m/s}\) when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of \(5.0 \times 10^5 \text{ kg}\), is blown straight backward with a speed of \(2.0 \times 10^6 \text{ m/s}\). A second piece, with mass \(8.0 \times 10^5 \text{ kg}\), continues forward at \(1.0 \times 10^6 \text{ m/s}\). What are the direction and speed of the third piece?