← Title screenSTATE OF THE ARC Arc smarter, not harder.

Two components. One clock.

Positive x points right; positive y points up. Height labels use the same datum, y = 0. Vertical displacement is target height minus launch height. Gravity g is a positive magnitude; vertical acceleration is −g.

For an angle θ above horizontal: vₓ = v cos θ and vᵧ₀ = v sin θ. Use degree mode. Horizontal velocity stays constant; vertical velocity changes under gravity. At the apex, only the vertical component is zero.

Use Δy = vᵧ₀t − ½gt², then Δx = vₓt. At equal heights discard t = 0. For a higher target level choose the later, descending crossing. A dashed target-level line is a reference, not a wall that blocks the upward crossing.

The stopwatch begins at release or firing. The projectile is modelled as a point at the marked launch position; its sprite and launcher are illustrations.

First component answers and first flight predictions are saved separately from corrections and completion. Lesson and practice records remain separate.

An interrupted flight stays paused until you choose Resume.