Projectile Motion Calculator Calculator
Calculates projectile motion parameters (range, max height, time) from initial velocity, angle, and height.
Info
Projectile motion occurs when an object is launched from a position at an angle to the horizontal. In the standard model, air resistance is ignored and only gravitational acceleration (g) acts. Key equations (2D, x-y plane): - Initial velocity components: vₓ = v₀ · cos(θ) vᵧ₀ = v₀ · sin(θ) - Position equations: x(t) = vₓ · t y(t) = y₀ + vᵧ₀ · t − ½ · g · t² - Flight time (positive root of y(t) = 0): t_f = (vᵧ₀ + √(vᵧ₀² + 2·g·y₀)) / g - Maximum height: t_peak = vᵧ₀ / g y_max = y₀ + vᵧ₀² / (2·g) This tool: - Finds flight time, range, and maximum height from v₀, θ, and y₀, - Samples the trajectory at regular intervals (Δt) and displays it in a table.
- Air resistance is ignored in this model; real-world range may be shorter.
- At 0° the motion is purely horizontal; at 90° it is purely vertical.
- If initial height (y₀) > 0, the object takes longer to fall and range may increase.
- For the same speed, maximum range (without air resistance) is achieved near 45° (when y₀ = 0).
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