Projectile Trajectory Calculator

Projectile Trajectory Equation:

\[ y = x \tan(\theta) - \frac{g x^2}{2 v^2 \cos^2(\theta)} \]

Horizontal Distance (x):

Angle (θ):

degrees

Initial Velocity (v):

m/s

Gravity (g):

m/s²

Vertical Distance (y):

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1. What is the Projectile Trajectory Equation?

The projectile trajectory equation calculates the vertical position (y) of a projectile at a given horizontal distance (x) based on launch angle (θ), initial velocity (v), and gravitational acceleration (g). It describes the parabolic path of objects under constant gravity with no air resistance.

2. How Does the Calculator Work?

The calculator uses the projectile trajectory equation:

\[ y = x \tan(\theta) - \frac{g x^2}{2 v^2 \cos^2(\theta)} \]

Where:

\( x \) — Horizontal distance (m)
\( \theta \) — Launch angle (degrees)
\( v \) — Initial velocity (m/s)
\( g \) — Gravitational acceleration (m/s²)
\( y \) — Vertical distance (m)

Explanation: The equation combines the linear motion component (x tanθ) with the gravitational acceleration component to determine the projectile's vertical position.

3. Importance of Projectile Trajectory Calculation

Details: Accurate trajectory calculation is essential for ballistics, sports physics, engineering applications, and understanding fundamental principles of motion in physics.

4. Using the Calculator

Tips: Enter horizontal distance in meters, angle in degrees (0-90), initial velocity in m/s, and gravitational acceleration (default 9.8 m/s²). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What assumptions does this equation make?
A: The equation assumes no air resistance, constant gravitational acceleration, and a flat Earth surface.

Q2: What is the maximum range of a projectile?
A: Maximum range occurs at a 45-degree launch angle with initial velocity v: R = v²/g.

Q3: How does air resistance affect trajectory?
A: Air resistance reduces both range and maximum height, making the trajectory asymmetrical rather than parabolic.

Q4: Can this be used for real-world applications?
A: While simplified, it provides a good approximation for many applications, though precise calculations may require accounting for air resistance and other factors.

Q5: What are typical values for initial velocity?
A: Varies widely: baseball pitch (40-45 m/s), golf drive (70-85 m/s), rifle bullet (600-1200 m/s).