To calculate the highest point of a soccer ball's trajectory, the initial velocity is 20 m/s at a 20-degree angle. The vertical component of the velocity can be determined using trigonometric functions, specifically by multiplying the initial velocity by the sine of the angle. The only force acting on the ball in the vertical direction is gravity, which accelerates it downward at 9.81 m/s². Using the equations of motion under uniform acceleration, the maximum height can be calculated by determining the time to reach the peak and substituting it back into the vertical motion equation. The discussion emphasizes the importance of focusing solely on the vertical component of motion to find the maximum height.