Final answer:
The time it takes for the ball to reach its maximum height is 1.6327 seconds, and the maximum height is approximately 12.94 meters.
Step-by-step explanation:
To find the time it takes for the ball to reach its maximum height, we can use the equation for vertical motion:
Final velocity (v) = Initial velocity (u) + (acceleration (a) * time (t))
When the ball reaches its maximum height, its final velocity will be 0 m/s. The initial velocity is 16 m/s (upward) and the acceleration due to gravity is -9.8 m/s² (downward). Plugging in these values, we get:
0 = 16 - 9.8 * t
Solving this equation for time, we find that t = 1.6327 seconds.
To find the maximum height, we can use the equation:
Final velocity^2 = Initial velocity^2 + 2 * acceleration * displacement
At the maximum height, the final velocity is 0 m/s, the initial velocity is 16 m/s, the acceleration is -9.8 m/s², and we want to find the displacement. Plugging in these values, we get:
0 = 16^2 + 2 * -9.8 * displacement
Simplifying, we find that the maximum height is approximately 12.94 meters.