// multi-utility computation suite · offline · instant · precise
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sci.projectile-motion-range Calculator
Calculates projectile range R = v₀² sin(2θ)/g, maximum height H = v₀² sin²(θ)/(2g), and time of flight T = 2v₀ sin(θ)/g. Maximum range occurs at θ = 45° — range at 45° is twice the maximum height, and range is symmetric: 30° and 60° give identical range.
Inputs
V0 M S
Speed in a specified direction (m/s). Required for momentum, kinetic energy, and wave calculations.
Theta Deg
Reference formula or conversion factor shown for context.
H0 M
Vertical measurement. For health calculators, typically standing height without shoes.
G M S2
Rate of velocity change (m/s²). Earth's gravity: 9.81 m/s². Objects in free fall accelerate at this rate.
Results
range R (m)
The difference between the maximum and minimum values.
max height H (m)
The computed height.
time of flight (s)
The computed duration or time value.
optimal angle (flat launch)
The computed angle in degrees or radians.
R = v₀²sin(2θ)/g (flat terrain)
The value at the specified point or condition.
with drag
Aerodynamic resistance opposing motion. Drag = 0.5 × rho × v^2 × Cd × A. Doubles with every 41% increase in speed (because it scales with v^2).