The net force on the cyclist is calculated by considering the forward force of 100N and the opposing forces of 50N from friction and 50N from air resistance. When these forces are combined, the equation is 100N + (-50N) + (-50N) = 0N, indicating no net force acting on the cyclist. This means the cyclist will maintain her speed of 20km/hr unless additional effort is applied or she slows down. The discussion emphasizes the importance of understanding how to apply Newton's laws to determine net force accurately. Ultimately, the net force on the cyclist is zero, allowing her to continue at a constant speed.