Motion in a Plane
12 topics · 12 interactive simulations
Vector Addition
Triangle and parallelogram law — add two vectors and read |R| and angle θ live.
Vector Components
Resolve a vector into Vₓ = V cosθ and Vᵧ = V sinθ with live projection lines.
Dot Product (Scalar)
A·B = |A||B|cosθ — see the projection of B onto A as theta varies.
Cross Product (Vector)
|A×B| = |A||B|sinθ — parallelogram area and right-hand rule direction.
Projectile Motion
Explore the physics of objects launched at an angle — trace trajectories, analyze velocity components, and understand range and height in real time.
Projectile: Angle Variation
Change angle θ and speed u — watch the parabola update and read R, H, T live.
Range vs Angle Curve
R = u²sin(2θ)/g — see the full curve and confirm max range at 45°.
Projectile from Height
Launch from a cliff — asymmetric trajectory with quadratic flight time.
Boat in a River
Boat velocity + river current — see the resultant path and drift angle.
Rain–Man Problem
Walker in vertical rain — compute umbrella tilt angle.
Uniform Circular Motion
Ball on a circle at constant ω — live v (tangent) and a (toward center) arrows.
Relative Motion
Visualize how motion appears different from different frames of reference. Understand relative velocity with interactive scenarios.