Final answer:
To calculate the curvature of the parabola formed by water ejected from a moving hose, one must analyze the velocity components using calculus, taking into account the hose's movement and changes in radius. However, the question does not provide enough information for a precise calculation.
Step-by-step explanation:
To calculate the curvature of the parabola formed by the ejected water flux when the hose is moved sideways with a given angular velocity, we should understand the relationship between linear velocity and angular velocity. The linear velocity v of an object moving in a circle is related to the angular velocity ω by the formula v = rω, where r is the radius of the circle. To find the curvature of the trajectory, we would need to look at the velocity components of the water at different points along its path and then use calculus to find the curvature at each point.
However, given that we are not provided with a specific mathematical model for the trajectory of the hose's end or the necessary variables to perform such a calculus-based analysis, a precise numerical answer cannot be given with the information provided. Generally, the curvature of a path is inversely proportional to the radius of the circular motion at any given point, and thus, as the hose moves, the radius of the curve made by the water jet would change, affecting the curvature of the parabola.