The G25 Distance Calculator is a tool designed to help you determine the horizontal range of a projectile launched at a specific angle and initial velocity, considering the effect of gravity. This is a fundamental concept in physics, particularly in the study of projectile motion.
The formula used in this calculator is derived from the kinematic equations of motion. For a projectile launched on a flat surface (where the launch height and landing height are the same), the horizontal distance (range) can be calculated using the following formula:
Range (R) = (v₀² * sin(2θ)) / g
Where:
v₀ is the initial velocity of the projectile (in meters per second).
θ is the launch angle with respect to the horizontal (in degrees).
g is the acceleration due to gravity (approximately 9.81 m/s² on Earth).
The calculator first converts the launch angle from degrees to radians, as trigonometric functions in most programming languages operate on radians. The value of sin(2θ) is then calculated. Finally, it plugs these values, along with the initial velocity and gravity, into the range formula to provide the horizontal distance.
How to Use the Calculator:
Initial Velocity (m/s): Enter the speed at which the projectile is launched.
Launch Angle (degrees): Input the angle (in degrees) relative to the ground at which the projectile is fired.
Acceleration due to Gravity (m/s²): This is typically set to 9.81 m/s² for Earth. You can change this value if you are calculating projectile motion on another celestial body.
Clicking the "Calculate Distance" button will display the calculated horizontal range in meters.
Example:
Let's say you launch a ball with an initial velocity of 50 m/s at a launch angle of 45 degrees. Assuming the standard acceleration due to gravity of 9.81 m/s², the calculator will compute:
This means the ball would travel approximately 254.84 meters horizontally before hitting the ground.
function calculateG25Distance() {
var initialVelocity = parseFloat(document.getElementById("initialVelocity").value);
var launchAngleDegrees = parseFloat(document.getElementById("launchAngle").value);
var gravity = parseFloat(document.getElementById("gravity").value);
var resultDiv = document.getElementById("result");
resultDiv.innerHTML = ""; // Clear previous results
if (isNaN(initialVelocity) || isNaN(launchAngleDegrees) || isNaN(gravity) || initialVelocity < 0 || gravity <= 0) {
resultDiv.innerHTML = "Please enter valid positive numbers for all fields. Gravity must be greater than 0.";
return;
}
if (launchAngleDegrees 90) {
resultDiv.innerHTML = "Launch angle must be between 0 and 90 degrees.";
return;
}
// Convert angle from degrees to radians
var launchAngleRadians = launchAngleDegrees * (Math.PI / 180);
// Calculate the range using the projectile motion formula
// R = (v₀² * sin(2θ)) / g
var range = (Math.pow(initialVelocity, 2) * Math.sin(2 * launchAngleRadians)) / gravity;
resultDiv.innerHTML = "