Motion in a Plane

Triangle and parallelogram law — add two vectors and read |R| and angle θ live.

Resolve a vector into Vₓ = V cosθ and Vᵧ = V sinθ with live projection lines.

A·B = |A||B|cosθ — see the projection of B onto A as theta varies.

|A×B| = |A||B|sinθ — parallelogram area and right-hand rule direction.

Explore the physics of objects launched at an angle — trace trajectories, analyze velocity components, and understand range and height in real time.

Change angle θ and speed u — watch the parabola update and read R, H, T live.

R = u²sin(2θ)/g — see the full curve and confirm max range at 45°.

Launch from a cliff — asymmetric trajectory with quadratic flight time.

Boat velocity + river current — see the resultant path and drift angle.

Walker in vertical rain — compute umbrella tilt angle.

Ball on a circle at constant ω — live v (tangent) and a (toward center) arrows.

Visualize how motion appears different from different frames of reference. Understand relative velocity with interactive scenarios.