Apparent Wind and Boat Speed: Vector Angle Construction (ApparentWind3)

This GeoGebra example demonstrates, in a 2D geometric setting, how changing wind direction affects the relationship between true/apparent wind and the boat’s speed by constructing and transforming velocity vectors. It centers on core ideas of planar vectors (addition/decomposition and direction handling), trigonometry (e.g., sine-based relations for angles or components), and geometric interpretation of speed and angle constraints. Construction-wise, it uses commands such as If and Rotate to handle conditional configurations and rotate the reference geometry, Circle to build speed/wind-related circles and obtain intersection points, and then represents the relevant quantities via generated objects like the wind/velocity vector W_{vel}, the boat velocity v, and labeled angle parameters such as TrueWindDirection and α. Supporting points and derived objects (e.g., O, A, V, G/H, and primed variants like pic1', G') help visualize multiple states and the resulting angle/velocity geometry. Suitable for upper secondary students and early university learners for vector-trigonometry visualization, physics-inspired modeling of wind/boat motion, and hands-on practice with geometric construction in GeoGebra.