Final answer:
The soccer ball travels a horizontal distance of 12.44 meters.
Step-by-step explanation:
To find the horizontal distance traveled by the soccer ball, we need to consider its initial speed and launch angle. We can break the initial velocity into its horizontal and vertical components using trigonometry.
The horizontal component of the initial velocity can be found using the equation Vx = Vi * cos(theta), where Vi is the initial speed and theta is the launch angle. Plugging in the values, we get Vx = 20 m/s * cos(59°) = 10.18 m/s.
Next, we can use the horizontal component of velocity and the equation d = Vx * t to find the horizontal distance. Since there is no air resistance, the time of flight will be the same as the time taken to reach the maximum height. Using the equation Vf = Vi + a * t and the fact that the final vertical velocity at the maximum height is 0 m/s, we can find the time taken. The equation simplifies to 0 = 12 m/s - 9.8 m/s^2 * t. Solving for t, we get t = 12 m/s / 9.8 m/s^2 = 1.22 s.
Finally, using the equation d = Vx * t, we can find the horizontal distance, which is d = 10.18 m/s * 1.22 s = 12.44 m.