Projectile Equation Calculator

Projectile Motion Equation:

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

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 Motion Equation?

The projectile motion equation calculates the vertical position (y) of a projectile at a given horizontal distance (x), based on launch angle (θ), initial velocity (v), and gravity (g). It describes the parabolic trajectory of objects under constant acceleration due to gravity.

2. How Does the Calculator Work?

The calculator uses the projectile motion equation:

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

Where:

\( x \) — Horizontal distance (m)
\( \theta \) — Launch angle (degrees)
\( v \) — Initial velocity (m/s)
\( g \) — Acceleration due to gravity (m/s²)
\( y \) — Vertical distance (m)

Explanation: The equation accounts for both the vertical component of the initial velocity and the effect of gravity on the projectile's trajectory.

3. Importance of Projectile Motion Calculation

Details: Understanding projectile motion is essential in physics, engineering, ballistics, and sports science. It helps predict the path of objects launched into the air under gravity's influence.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: What is the maximum height equation?
A: Maximum height is given by \( h_{max} = \frac{v^2 \cdot \sin^2(\theta)}{2g} \), reached when vertical velocity becomes zero.

Q2: What is the range equation?
A: The horizontal range is \( R = \frac{v^2 \cdot \sin(2\theta)}{g} \), which gives the total horizontal distance traveled.

Q3: Does air resistance affect the calculations?
A: Yes, this equation assumes no air resistance. In reality, air resistance reduces both range and maximum height.

Q4: What is the time of flight?
A: Time of flight is \( T = \frac{2v \cdot \sin(\theta)}{g} \), representing the total time the projectile remains in the air.

Q5: Can this be used for objects launched from height?
A: This equation assumes launch from ground level. For objects launched from height, the equation needs modification to account for initial height.