# Projectile Motion Calculator

Select the parameter to be calculated (time of flight, height, or range) and provide the required ones against it. The calculator will readily calculate its value, with the steps shown.

Projectile motion calculator computes the velocity, height, and flight duration at a given time. This Projectile calculator analyzes the parabolic motion and solves a special case where an object is launched from an elevated plane horizontally.

## What is Projectile Motion?

In physics, a projectile motion is defined as the motion of an object thrown into the air and subjected to gravitational acceleration. The path followed by the object is called the trajectory, while an object is indicted as the projectile, and the movement of the object is called the motion of the projectile.

### Projectile Motion Equations:

The most essential projectile motion equations are: Projecting an object from the earth surface, where initial height h = 0 Horizontal velocity component: $$V_{x} = cos\left(α\right) * V$$ Vertical velocity component: $$V_{y} = sin\left(α\right) * V$$ Flight duration: $$t = \dfrac{V_{y}}{g} * 2$$ Range of the projectile: $$R = \dfrac{V_{y}}{g} * V_{x} * 2$$ Maximum height: $$\text{max h} = \dfrac{V_{y}^{2}}{2 * g}$$ Projecting the object from some height where initial height h > 0 Horizontal velocity component: $$V_{x} = cos\left(α\right) * V$$ Vertical velocity component: $$V_{y} = sin\left(α\right) * V$$ Time of flight: $$t = \dfrac{\sqrt{\left(Vy^{2} + 2 * g * h\right)} + V_{y}}{g}$$ Range of the projectile: $$R = V_{x} * \dfrac{\sqrt{\left(V_{y}^{2} + 2 * g * h\right)} + V_{y}}{g}$$ Maximum height: $$\text{h max} = V_{y}^{2} + \dfrac{h}{2 * g}$$

## How Projectile Motion Calculator Works?

### Input:

• Firstly, choose an option from the drop-down list, which you need to calculate the projectile motion with that particular parameter.
• Now, substitute the values according to the selected option.
• Click on the "Calculate" button to determine the projectile.

### Output:

The Calculator calculates:
• Initial Horizontal Velocity (Vx)
• Initial Vertical Velocity (Vy)
• Gravitational Acceleration
If you select the flight parameters at a given time from the drop-down list, then it'll provide:
• Horizontal Position
• Height

## Reference:

From the source of Wikipedia: Kinematic quantities of projectile motion, Trajectory of a projectile with air resistance, Trajectory of a projectile with Stokes drag, Trajectory of a projectile with Newton drag, Lofted trajectory.