Trajectory Calculator

Using the Trajectory Calculator

Welcome to the Trajectory Calculator guide! This tool allows you to calculate various parameters of a projectile’s trajectory, such as maximum height, time of flight, horizontal range, and initial velocities. Follow these steps to correctly use the calculator and interpret its results.

Step 1: Enter Inputs

• Initial Velocity (m/s): Enter the initial speed of the projectile in meters per second. The field will only accept values from 0 to 1000, with increments of 0.1. Ensure that you do not leave this field empty as it is required.
• Launch Angle (degrees): Input the angle at which the projectile is launched relative to the horizontal. The angle should be between 0 and 90 degrees. Use increments of 0.1 degrees for precise measurements.
• Initial Height (m): Specify the initial height from which the projectile is launched, in meters. This value can range from 0 to 1000 and is required to ensure accurate calculations.
• Gravitational Acceleration: Select the appropriate gravitational acceleration for the context of your problem. You have three options:
  • Earth: 9.81 m/s²
  • Moon: 1.62 m/s²
  • Mars: 3.72 m/s²

  Make sure to select one, as this is a required field.

Step 2: Reviewing the Results

After inputting all the necessary data fields, the calculator will provide the following results:

• Maximum Height: The highest point reached by the projectile measured in meters. This value takes into account the initial height and is calculated with the formula: initialHeight + (pow(initialVelocity * sin(angle * pi / 180), 2)) / (2 * gravity).
• Time of Flight: The total time the projectile stays in the air before touching down, given in seconds. The formula used is: (initialVelocity * sin(angle * pi / 180) + sqrt(pow(initialVelocity * sin(angle * pi / 180), 2) + 2 * gravity * initialHeight)) / gravity.
• Horizontal Range: The distance covered by the projectile along the horizontal plane in meters. Calculated as: initialVelocity * cos(angle * pi / 180) * ((initialVelocity * sin(angle * pi / 180) + sqrt(pow(initialVelocity * sin(angle * pi / 180), 2) + 2 * gravity * initialHeight)) / gravity).
• Initial Horizontal Velocity: The component of the initial velocity in the horizontal direction, measured in meters per second. Calculated using: initialVelocity * cos(angle * pi / 180).
• Initial Vertical Velocity: The component of the initial velocity in the vertical direction, also measured in meters per second. Determined via: initialVelocity * sin(angle * pi / 180).

Ensure to carefully check and record these results as they provide valuable insights into the projectile’s behavior.

Conclusion

Using the Trajectory Calculator is straightforward if each step is carefully followed and accurate inputs are provided. This tool is excellent for physics students, engineers, or anyone interested in understanding projectile motion. Experiment with different values to see the effect on the projectile’s trajectory.