Ball Velocity as x and y components

First: The diagonal line to the red ball represents the ball's velocity. The magnitude of the velocity is fixed at 400 units but the direction may be changed by moving the slider. When moving the slider the ball moves around the circle of radius 400 shown because its velocity magnitude is fixed at 400. The velocity may be projected in both x and y directions, as shown, depending on the angle of direction which is shown at bottom left: the x velocity is then 400*cos(angle) and the y velocity is 400*sin(angle).

Second: The x and y velocities may be projected back on the direction of travel of the ball. Then the contribution due to the x projection is cos(angle) times the x velocity or 400*cos2(angle) and the contribution due to the y projection is 400*sin2(angle), as shown. Observe that since cos2(angle)+sin2(angle)=1, the sum of the two projections is 400.