1. Understand the Physics

* Projectile Motion: The soccer ball's motion is a projectile, meaning it's influenced by gravity. We need to consider both horizontal and vertical components of its motion.

* Horizontal Velocity: The horizontal velocity remains constant throughout the flight.

* Vertical Velocity: The vertical velocity is affected by gravity, slowing down as the ball rises and speeding up as it falls.

2. Break Down the Initial Velocity

* Horizontal Component (Vx): Vx = V * cos(theta) = 26 m/s * cos(30°) ≈ 22.5 m/s

* Vertical Component (Vy): Vy = V * sin(theta) = 26 m/s * sin(30°) = 13 m/s

3. Calculate the Time of Flight

* Symmetry: The time it takes for the ball to go up is equal to the time it takes to come down.

* Vertical Motion: We can use the following kinematic equation:

Vyf = Vy + at, where:

* Vyf = final vertical velocity (0 m/s at the highest point)

* Vy = initial vertical velocity (13 m/s)

* a = acceleration due to gravity (-9.8 m/s²)

* t = time

* Solving for t: 0 = 13 - 9.8t

t ≈ 1.33 s (This is the time to reach the highest point, double it for the total time of flight)

Total time of flight ≈ 2.66 s

4. Calculate the Horizontal Distance (Range)

* Range: Range = Horizontal Velocity * Time of flight

* Range: Range ≈ 22.5 m/s * 2.66 s ≈ 59.85 m

Answer: The soccer ball travels approximately 60 meters before hitting the ground.