Final answer:
The maximum height depends on initial velocity and resistance coefficient, but a specific formula requires additional information for integration.
Step-by-step explanation:
To find the maximum height attained by the ball, we need to consider the point where kinetic energy is fully converted to potential energy. Because the upward force of the throw and gravity are acting in opposite directions, the resistive force is also opposite the motion during the ascent.
The resistive force proportional to kv2 means that as the ball travels upward, the resistive force increases with the square of the velocity. Nonetheless, the resistive force will eventually reduce the velocity to zero at the maximum height.
Without an explicit expression for height in terms of the initial velocity and resistance proportionality constant, we cannot provide a numerical answer to this question. The determination of the maximum height must involve integrating the forces with respect to the displacement, accounting for the gravitational force and the resistive force.
In summary, the maximum height achieved by the ball depends on the initial velocity and the coefficient of the resistive force, but cannot be given by a straightforward formula without further information.