Enter your initial velocity, launch angle, and other parameters into the calculator to determine the trajectory of the projectile.

## Trajectory Calculation Formula

The following formula is used to calculate the range of a projectile:

Range = (Initial Velocity² * sin(2 * Launch Angle)) / g

Variables:

- Range is the horizontal distance traveled by the projectile (m)
- Initial Velocity is the speed at which the projectile is launched (m/s)
- Launch Angle is the angle at which the projectile is launched (degrees)
- g is the acceleration due to gravity (approximately 9.81 m/s²)

To calculate the range, you need to know the initial velocity and the launch angle. The sine function is used to account for the angle of launch, which affects how far the projectile will travel.

## What is Projectile Motion?

Projectile motion refers to the motion of an object that is thrown into the air and is subject to the force of gravity. The path that the object follows is called its trajectory, which is typically a parabolic shape. Understanding projectile motion is essential in various fields, including physics, engineering, and sports science.

## How to Calculate Trajectory?

The following steps outline how to calculate the trajectory of a projectile using the given formula:

- Determine the initial velocity of the projectile.
- Measure the launch angle at which the projectile is fired.
- Use the formula provided to calculate the range.
- Consider the effects of initial height and gravity if using the advanced calculator.
- Check your results with the calculator above for accuracy.

**Example Problem:**

Use the following variables as an example problem to test your knowledge.

Initial Velocity = 50 m/s

Launch Angle = 45 degrees

Initial Height = 0 m

## FAQ

**1. What factors affect the trajectory of a projectile?**

The trajectory of a projectile is affected by its initial velocity, launch angle, air resistance, and the acceleration due to gravity.

**2. How does the launch angle influence the range?**

The launch angle significantly influences the range; typically, a launch angle of 45 degrees yields the maximum range in a vacuum.

**3. Can this calculator be used for different heights?**

Yes, the advanced calculator allows you to input the initial height to calculate the trajectory accurately.

**4. Is the calculator accurate for real-world applications?**

The calculator provides an estimate of the trajectory based on ideal conditions. For real-world applications, factors like air resistance should be considered.

**5. How often should I use the trajectory calculator?**

It’s helpful to use the trajectory calculator whenever you need to analyze projectile motion in sports, engineering, or physics experiments.