Final answer:
The ratio of the kinetic energies of a rocket when its velocity is suddenly tripled is 9:1. This is because kinetic energy is proportional to the square of the velocity.
Step-by-step explanation:
If a rocket is moving up with a velocity v, and its velocity is suddenly tripled, the ratio of the two kinetic energies can be calculated using the kinetic energy formula KE = 1/2 m v^2. Let's denote the initial kinetic energy as KE1 and the kinetic energy after tripling the velocity as KE2.
The initial kinetic energy is KE1 = 1/2 m v^2. After tripling the velocity, the new velocity is 3v, so the new kinetic energy is KE2 = 1/2 m (3v)^2 = 9/2 m v^2. To find the ratio of the two kinetic energies, we divide KE2 by KE1:
KE2/KE1 = (9/2 m v^2) / (1/2 m v^2) = 9.
Therefore, the ratio of the two kinetic energies is 9:1, meaning that the kinetic energy after tripling the velocity is nine times greater than the initial kinetic energy.