# Projectile Motion Calculator

Welcome to the Projectile Motion Calculator! This tool enables you to compute essential parameters involved in projectile motion, such as time of flight, horizontal range, and maximum height. Whether you’re a student studying physics or simply curious about the dynamics of projectile motion, this calculator provides a quick and efficient way to perform these calculations.

To get started, input the initial velocity (v<sub>0</sub>) and the launch angle (θ). Then, click “Calculate” to obtain the results. Understanding the behavior of projectiles has never been easier.

Efficient, informative, and user-friendly — that’s what this Projectile Motion Calculator is all about. Begin by entering your values above and hit “Calculate” to explore the fascinating world of projectile motion. Happy calculating!

## Projectile Motion Calculations

## Horizontal Motion:

The horizontal component of velocity (V_{ix}) is given by:
V_{ix} = V_{i} × cos(angle)
where V_{i} is the initial velocity (30 m/s) and the angle is given as 30 degrees.
V_{ix} ≈ 26.0 m/s

The horizontal range (R) can be calculated using the formula:
R = (V_{ix} × 2V_{i}) / g
where g is the acceleration due to gravity (approximately 9.81 m/s^{2}).
R ≈ 79.36 meters

### Vertical Motion:

The vertical component of velocity (V_{iy}) is given by:
V_{iy} = V_{i} × sin(angle)
V_{iy} ≈ 15 m/s

The time (t) taken to reach the maximum height can be calculated using the formula:
t = V_{iy} / g
t ≈ 1.53 seconds

The maximum height (H) can be calculated using the formula:
H = (V_{iy}^{2}) / (2g)
H ≈ 11.47 meters

So, for the given initial velocity of 30 m/s and an angle of 30 degrees in a projectile motion:

- The horizontal range is approximately 79.36 meters.
- The maximum height reached is approximately 11.47 meters.
- The time taken to reach the maximum height is approximately 1.53 seconds.