Final answer:
The maximum height reached by the ball is approximately 0.27 meters.
Step-by-step explanation:
To find the maximum height reached by the ball, we need to analyze its vertical motion. When an object is thrown vertically, the initial vertical velocity determines its maximum height. In this case, the ball has an initial vertical velocity of 2.3 m/s. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can find the time it takes for the ball to reach its maximum height. Considering the ball's motion upwards, its final velocity at its maximum height is 0. Therefore, we have 0 = 2.3 m/s - 9.8 m/s^2 * t. Solving for t, we find that it takes approximately 0.235 seconds for the ball to reach its maximum height.
To find the maximum height, we can use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement. Since the ball reaches a point where it is momentarily at rest at its maximum height, the final velocity is 0. Plugging in the values, we have 0 = (2.3 m/s)^2 - 2 * 9.8 m/s^2 * s.
Simplifying the equation, we get 5.29 m^2/s^2 = 19.6 m/s^2 * s. Solving for s, we find that the maximum height reached by the ball is approximately 0.27 meters. Therefore, the maximum height reached by the ball is approximately 0.27 meters.