To determine the height the ball reaches, we can use the equations of motion under constant acceleration. When the ball is thrown straight upward, it experiences a constant acceleration due to gravity, which acts in the opposite direction to its initial velocity.
The equation that relates the displacement, initial velocity, time, and acceleration is given by:
s = Vi * t - (1/2) * g * t^2
Where: s is the displacement or height of the ball, Vi is the initial velocity (15 m/s), t is the time, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
At the highest point of the ball's trajectory, its final velocity (Vf) becomes zero. Therefore, we can use this fact to determine the time it takes for the ball to reach its highest point.
Vf = Vi - g * t
0 = 15 - 9.8 * t
Solving for t:
9.8 * t = 15
t = 15 / 9.8
t ≈ 1.53 seconds
Now that we have the time it takes for the ball to reach its highest point, we can substitute this value into the equation for displacement:
s = Vi * t - (1/2) * g * t^2
s = 15 * 1.53 - (1/2) * 9.8 * (1.53)^2
s ≈ 11.48 meters
Therefore, the ball reaches a height of approximately 11.48 meters in the air before it starts descending.