Final answer:
The rocket carrying fireworks will initially follow a trajectory determined by its propulsion and gravity. Upon explosion, the fireworks fragments will retain their horizontal motion and also be influenced by gravity and air resistance. The correct answer is C) They follow the rocket's trajectory.
Step-by-step explanation:
When a rocket carrying fireworks is launched from a hill and later explodes, the fireworks will follow the rocket's initial trajectory until the explosion. At the point of explosion, the kinetic energy of the rocket is converted into the thermal energy, sound, and the kinetic energy of the individual fireworks fragments. These pieces will begin to move outward in all directions due to the conservation of momentum and the center of mass principle.
Initially, the rocket moves with constant acceleration upwards, under the influence of the rocket's propulsion and the force of gravity. According to Newton's first law of motion, an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. When the fireworks explode, each piece will retain the horizontal component of the velocity it had at the moment of explosion. However, they will also start falling downward due to gravity, resulting in a parabolic trajectory of each fragment.
The motion of the shell and its fragments prior to and after the explosion can be better understood through principles of projectile motion and air resistance. Air resistance significantly affects the fragments after the explosion, leading many of them to fall directly below the initial trajectory. The horizontal motion before the explosion is performed at a constant velocity, assuming negligible air resistance. This horizontal displacement is useful for safety purposes, ensuring the fragments don't fall on spectators.
In terms of changes to motion at the explosion, the center of mass of the fireworks will continue on the same path as the unexploded shell if there were no air resistance. However, with the introduction of air resistance post-explosion, the path of the center of mass will likely alter slightly since the smaller fragments have more surface area relative to their mass, causing them to slow down more quickly than the intact shell would.
The option that is correct for what happens to the fireworks after the rocket explodes is C) They follow the rocket's trajectory.