Final answer:
The ratio of the speeds UA/UA' at the same point in two different cases would be 1, assuming similar conditions and no unspecified external factors altering the situation.
Step-by-step explanation:
The student is asking about comparing speeds UA/UA' at points A and A' under two different conditions. This situation seems to be a physics problem involving the principles of mechanics and possibly fluid dynamics, given the reference to velocities and nozzles. Without additional context, UA/UA' should theoretically be equal if 'A' and 'A'' refer to the same physical point under similar conditions. Therefore, the ratio of the speeds UA/UA' would be 1.
If the velocity at point A is denoted by V₁ or v for two different cases, the answer to what the ratio of the speeds UA/UA' is, would be 1, assuming no external factors are altering the conditions at point A that have not been specified in the question.