Final answer:
Without specific data on the velocity and altitude at the point of separation, it is not possible to give exact figures for the booster's behavior. However, the booster will follow a ballistic trajectory governed by gravity and aerodynamic drag until returning to Earth according to the principles of projectile motion and Newton's laws.
Step-by-step explanation:
To determine how high and how fast a rocket booster goes after being released, it is essential to know the velocity and altitude at the moment of separation. Without these specifics, we can only discuss the general principles that apply. Upon release, the booster's trajectory will be influenced by the velocity it had at separation and the forces acting upon it, primarily gravity and aerodynamic drag. The booster will continue on a ballistic trajectory, with its altitude initially increasing until the vertical component of its velocity slows to zero due to gravity, at which point it will begin to fall back to Earth. Speed-wise, it will gradually decrease as drag opposes its motion. Without explicit numerical data, providing a precise altitude and velocity is not feasible. However, the principles of projectile motion and Newton's laws of motion are what dictate the booster's behavior until it impacts the ground or is slowed sufficiently for a controlled descent if such a system is in place.