Final answer:
Physics principles such as momentum conservation and kinematics are used to calculate the ball's height and flight duration. Provided information hints at a two-dimensional problem, but lacks details required for a comprehensive solution.
Step-by-step explanation:
The question you've asked involves calculations based on the principles of physics, specifically kinematics and energy conservation. Since you have provided information about the force impulse given to the ball (150 kg·m/s), we can deduce the initial velocity using the relation impulse = mass · velocity change. In this scenario, to find how high the ball goes, we utilize the conservation of energy principle, while the duration of the flight and the horizontal distance can be determined by kinematic equations.
It is important to clarify that the provided information seems to have some inconsistencies. The force of 150 kg·m/s is actually an impulse (mass · velocity), not a force (mass · acceleration). Moreover, it mentions a gust of wind affecting horizontal velocity, which suggests the problem might be a two-dimensional motion question, but the original query only asks for height and flight time, typically associated with vertical motion. If we are considering horizontal displacement factor, additional details such as wind impact duration would be necessary to provide a complete answer.