[ // Free fall distance (vertical) { name: "Free Fall Distance", description: ''' Calculates vertical displacement under constant gravity `h = ½gt²` Where: - `g` = Gravitational acceleration (9.81 m/s² on Earth) - `t` = Time in free fall (seconds) ![Free Fall Diagram](https://upload.wikimedia.org/wikipedia/commons/thumb/7/72/Free-fall.svg/1200px-Free-fall.svg.png)''', input: [ {name: "t", unit: "s"}, // Time in seconds {name: "g", unit: "m/s²"} // Gravitational acceleration ], output: {name: "h", unit: "m"}, // Height in meters d4rtCode: "h = 0.5 * g * pow(t, 2)" }, // Newton's Law of Universal Gravitation { name: "Gravitational Force", description: ''' Newton's law of universal gravitation `F = G(m₁m₂)/r²` Where: - `G` = Gravitational constant (6.674×10⁻¹¹ N·m²/kg²) - `m₁`, `m₂` = Masses of two objects - `r` = Distance between centers of masses ![Gravitation](https://upload.wikimedia.org/wikipedia/commons/thumb/3/33/NewtonsLawOfUniversalGravitation.svg/1200px-NewtonsLawOfUniversalGravitation.svg.png)''', input: [ {name: "m1", unit: "kg"}, // Mass 1 {name: "m2", unit: "kg"}, // Mass 2 {name: "r", unit: "m"} // Distance between masses ], output: {name: "F", unit: "N"}, // Force in newtons d4rtCode: "F = (6.67430e-11 * m1 * m2) / pow(r, 2)" }, // Kinetic Energy { name: "Kinetic Energy", description: ''' Energy possessed by a moving object `KE = ½mv²` Where: - `m` = Mass of object - `v` = Velocity of object ![Kinetic Energy](https://upload.wikimedia.org/wikipedia/commons/thumb/4/44/Kinetic_energy.svg/1200px-Kinetic_energy.svg.png)''', input: [ {name: "m", unit: "kg"}, // Mass {name: "v", unit: "m/s"} // Velocity ], output: {name: "KE", unit: "J"}, // Energy in joules d4rtCode: "KE = 0.5 * m * pow(v, 2)" }, // Projectile Motion Range { name: "Projectile Range", description: "Calculates horizontal distance of projectile motion\n\n" "`R = (v² sin(2θ))/g`\n\n" "Where:\n" "- `v` = Initial velocity\n" "- `θ` = Launch angle\n" "- `g` = Gravitational acceleration\n\n" "![Projectile Motion](https://upload.wikimedia.org/wikipedia/commons/thumb/5/52/Projectile_motion_diagram.png/800px-Projectile_motion_diagram.png)", input: [ {name: "v", unit: "m/s"}, // Initial velocity {name: "θ", unit: "deg"} // Launch angle ], output: {name: "R", unit: "m"}, // Horizontal distance d4rtCode: "R = (pow(v, 2) * sin(2 * radians(θ))) / 9.80665" }, { name: "Newton's Second Law", description: ''' Force equals mass times acceleration `F = m * a` Where: - `m` = Mass of object (kg) - `a` = Acceleration (m/s²) ![Newton's Second Law](https://upload.wikimedia.org/wikipedia/commons/thumb/7/73/Newtonslawsofmotion.jpg/800px-Newtonslawsofmotion.jpg)''', input: [ {name: "m", unit: "kg"}, // Mass {name: "a", unit: "m/s²"} // Acceleration ], output: {name: "F", unit: "N"}, // Force in newtons d4rtCode: "F = m * a" }, ]