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Spaceship motion involves understanding how an object's movement changes due to external forces. In outer space, without the resistance of air or friction, a spaceship will continue moving at a constant speed and direction unless acted upon by another force. This behavior is an example of Newton's First Law of Motion — or the principle of inertia. As seen in our exercise, the spaceship first travels seamlessly through space at a speed of \(5.0 \times 10^{6} \mathrm{m/s}\).
An essential aspect of spaceship motion is calculating momentum, which helps predict how the motion changes when influenced by forces such as explosions. In our example, the spaceship's momentum is the product of its mass \(2.0 \times 10^{6} \mathrm{kg}\) and its initial velocity \(5.0 \times 10^{6} \mathrm{m/s}\). Understanding these dynamics is crucial as it forms the basis for analyzing any changes to the motion, like when the ship experiences an explosion.

Explosion dynamics concentrates on the effects of a rapid expansion of energy, causing an object to break into multiple parts. In the case of our spaceship, the explosion results in the ship splitting into three pieces. This type of explosion illustrates the conservation of momentum, where the total momentum before the explosion equals the total momentum after the explosion.
When the spaceship's antimatter reactor fails, energy is released dramatically. This energy influences the speed and direction of the space pieces. It's crucial to know that despite the massive forces involved, the explosion does not create or destroy momentum; it merely redistributes it among the pieces.

• The first piece is affected by the explosion by being pushed backward with a speed of \(2.0 \times 10^{6} \mathrm{m/s}\).
• The second piece continues its journey forward at \(1.0 \times 10^{6} \mathrm{m/s}\).

Understanding explosion dynamics is key to calculating and predicting the behavior of each piece after the event.

Momentum calculation is a fundamental concept for solving the problem of how the pieces of the exploded spaceship move. Momentum, a vector quantity, is calculated by multiplying an object's mass by its velocity.
In the context of the spaceship, the total momentum before the explosion (\(1.0 \times 10^{13} \mathrm{kg.m/s}\)) must equal the total momentum after. Calculating momentum for each piece involves accounting for both magnitude and direction.

• The first piece has a negative momentum because it moves in the opposite direction \((-1.0 \times 10^{12} \mathrm{kg.m/s})\).
• The momentum of the second piece remains positive \(8.0 \times 10^{11} \mathrm{kg.m/s}\).

Finally, finding the velocity of the third piece involves using the momentum equation, where the sum of the momentum of the first two pieces is subtracted from the total initial momentum. Incorporating these calculations ensures we respect the conservation of momentum principle, ultimately allowing us to solve for unknown velocities and directions effectively.