Final answer:
The initial velocity is the key factor that dictates the rocket's trajectory after launch. Thrust and rocket mass are also critical in influencing the rocket's ongoing path and acceleration, but the question specifically asks about the initial trajectory.
Step-by-step explanation:
The primary factor determining the rocket's trajectory after it has been fired at a speed of 75 m/s is the initial velocity. This is because the rocket's path is mostly shaped by its speed and direction at the point of launch, assuming no significant external forces act on it after liftoff. However, it's also important to note that other forces will come into play during the rocket's flight, such as thrust generated by expelled fuel, which continuously propels the rocket forward, and the force of gravity acting upon it.
The three main factors affecting a rocket's acceleration include the exhaust velocity of the gases (Ve), the rate of ejected mass (∆m/∆t), and the rocket's remaining mass (m). During flight, as the rocket burns fuel and the mass decreases, the acceleration generally increases, reaching a maximum just before the fuel is exhausted. Therefore, while the initial velocity is the primary factor that sets the rocket's initial path, thrust and rocket mass also play crucial roles in the ongoing trajectory and acceleration of the rocket.