[ // Free fall distance (vertical) { "name": "Free Fall Distance", "description": r""" Calculates vertical displacement under constant gravity $$h = \frac{1}{2}gt^2$$ Where: - $g$: Gravitational acceleration $9.81\ \mathrm{m/s^2}$ on Earth - $t$: Time in free fall (seconds) ![Free Fall Diagram](https://altcalculator.com/wp-content/uploads/2023/08/Free-Fall.png)""", "input": [ {"name": "t", "unit": "second"}, // Time in seconds {"name": "g", "unit": "meters per second"} // Gravitational acceleration ], "output": {"name": "h", "unit": "meter"}, // Height in meters "d4rtCode": "h = 0.5 * g * pow(t, 2);", "tags": ["physics", "kinematics"] }, // Newton's Law of Universal Gravitation { "name": "Gravitational Force", "description": r''' Newton's law of universal gravitation \(F = G\frac{m_1m_2}{r^2}\) Where: - $G$: Gravitational constant $6.674\times 10^{-11}\ \mathrm{N\cdot m^2/kg^2}$ - $m_1, m_2$: 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": "kilogram"}, // Mass 1 {"name": "m2", "unit": "kilogram"}, // Mass 2 {"name": "r", "unit": "meter"} // Distance between masses ], "output": {"name": "F", "unit": "newton"}, // Force in newtons "d4rtCode": "F = (6.67430e-11 * m1 * m2) / pow(r, 2);", "tags": ["physics", "astronomy", "gravity"] }, ]