Final answer:
In a fireworks display, light from the explosion is seen before the sound is heard due to the different speeds at which light and sound travel. In deep space, the absence of gravity and air resistance would mean that the fragments would continue moving outward indefinitely, maintaining the conservation of momentum and the position of the center of mass.
Step-by-step explanation:
Dynamics of Firework Explosions
When a person is standing 0.5 km away from a fireworks display, they would first see the light from the explosion due to the high speed of light. Shortly after, they would hear the sound, which travels more slowly. The lag between seeing the light and hearing the sound would be noticeable. In deep space, far from any gravity source, the fireworks would not fall back to Earth as they do in our atmosphere. Instead, once they explode, the fragments would travel outward indefinitely in all directions, due to the conservation of momentum. The center of mass of the system, consisting of the explosive fragments, would remain stationary if there were no external forces acting on it. This difference is because, in space, there is no air resistance or gravitational pull to decelerate and pull the fragments back down as on Earth.
In terms of the physics involved, a fireworks projectile typically as an initial velocity and is ignited at its highest point, where its height, time of flight, and horizontal displacement can be calculated using kinematic equations.