Final answer:
The time interval for the ball to reach its maximum height of 5.7 m under gravity acceleration of 9.8 m/s² is approximately 1.08 seconds using the kinematic equations for uniform acceleration.
Step-by-step explanation:
The question asks what the time interval between the release of the ball and the time it reaches its maximum height is, given the maximum height (5.7 m) and the acceleration due to gravity (9.8 m/s2). To calculate the time interval, we can use the kinematic equations for uniform acceleration, specifically, the equation that relates distance (s), initial velocity (u), acceleration (a), and time (t): s = ut + (1/2)at2.
At maximum height, the final velocity (v) is 0 m/s because the ball has momentarily stopped before starting to fall back down. Since the initial upward velocity (u) is not given, we can rearrange the kinematic equation to solve for time (t) using the given maximum height (s) and acceleration (a). After rearranging, we get t = sqrt(2s/a). Plugging in the values s = 5.7 m and a = 9.8 m/s2, we find t = sqrt((2*5.7)/9.8), which calculates to approximately 1.08 seconds.
This is the time interval for the ball to reach its maximum height after being released.