y-Component from Magnitude and Angle
Worked example: Magnitude 20 at 30° → v_y = 10 — press Try an example to run it live, then adjust anything.
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Grade 12Grade 12 Math
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y-Component from Magnitude and Angle explained
The vertical partner of the x-component: |v| sin θ is how much of the arrow points up. A projectile launched at 40 m/s and 30° leaves the muzzle with 40 × sin 30° = 20 m/s of upward speed, and that number alone — not the 40 — decides how high and how long it flies. Together the pair (|v| cos θ, |v| sin θ) is the machinery that lets you replace one awkward diagonal with two independent one-dimensional problems, which is the reason vectors earn their place in physics at all.
Solving for the angle uses arcsin, whose principal branch runs only from −90° to 90°. A vector at 150° has the same y-component as one at 30°, so formula.expert returns the first-quadrant answer; if you know the vector leans left, its true direction is 180° minus what you get. When the whole vector is horizontal, sin θ = 0 and no y-component can tell you how long it is.
y-Component from Magnitude and Angle formula
- = y-component
- = Vector magnitude
- = Angle from +x axis (°)
Missing one of these? Work it out first, then come back
- y-component — x-Component from Magnitude and Angle, Direction Angle of a 2D Vector
- Vector magnitude — x-Component from Magnitude and Angle, Unit Vector Component (Normalization)
- Angle from +x axis — x-Component from Magnitude and Angle, Direction Angle of a 2D Vector