Speed at Any Instant — Recombining the Components
Freeze a horizontal throw anywhere in its flight and read the velocity triangle drawn at that instant: the horizontal component never changes, the vertical one grows by g every second, and the speed is the hypotenuse of the two — never their sum. 14.7 and 19.6 combine to 24.5, and the energy route agrees to the same decimal.
Como usar esta simulação
- Drag the time slider to freeze the throw anywhere and read the triangle
- Set the launch speed and the drop height to any pair of values
- Load the worked example — 14.7 m/s from 19.6 m, arriving at 24.5 m/s
- Press Dropped, not thrown to collapse the triangle to its vertical side alone
O que observar
- The horizontal side of the triangle has the same length at every instant
- The vertical side grows by g each second, so the hypotenuse turns steadily downwards
- The speed is always less than the two components added together, and more than either alone
- The time route and the energy route give the same impact speed every time
- With zero launch speed the triangle degenerates and the speed is purely vertical
A física por trás
The two components evolve independently: vₓ = v₀ stays fixed because nothing pushes horizontally, while vᵧ = gt grows steadily from rest. The speed at any instant is their resultant, v = √(vₓ² + vᵧ²), which is why adding the components arithmetically always overestimates it. Substituting the fall relation vᵧ² = 2gh gives the alternative form v = √(v₀² + 2gh), the same result reached through energy rather than time. Both routes must agree, since they describe one motion.