Final answer:
When a ball is thrown vertically upward with a speed of 19.0 m/s, it will reach a maximum height of approximately 18.47 meters.
Step-by-step explanation:
When a ball is thrown vertically upward, its initial velocity is positive, but its acceleration due to gravity is negative. The ball will rise until its velocity becomes 0, and then it will start to fall back down.
To find the maximum height the ball reaches, we can use the kinematic 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.
In this case, the final velocity is 0 because the ball reaches its maximum height and stops momentarily before falling back down. The initial velocity is 19.0 m/s, the acceleration due to gravity is -9.8 m/s^2, and we are trying to find the displacement (maximum height).
Plugging in the values into the equation:
0 = (19.0)^2 + 2(-9.8)S
Simplifying the equation:
0 = 361 - 19.6S
Moving the terms around:
19.6S = 361
Solving for S:
S = 361/19.6
Simplifying the value:
S ≈ 18.47 m
Therefore, the ball reaches a maximum height of approximately 18.47 meters.