Projectile Motion Calculator

Projectile Motion Formulas:

\[ x = v_0 \cdot \cos(\theta) \cdot t \] \[ y = v_0 \cdot \sin(\theta) \cdot t - \frac{1}{2} \cdot g \cdot t^2 \]

Where:
x: Horizontal distance (m)
y: Vertical distance (m)
v₀: Initial velocity (m/s)
θ: Launch angle (degrees)
t: Time (s)
g: Gravitational acceleration (9.81 m/s²)

Horizontal Distance (x):

Vertical Distance (y):

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1. What is a Projectile Motion Calculator?

Definition: This calculator computes the horizontal and vertical positions of a projectile at a given time based on initial velocity and launch angle.

Purpose: It helps physics students, engineers, and sports professionals analyze projectile trajectories for various applications.

2. How Does the Calculator Work?

The calculator uses the projectile motion equations:

\[ x = v_0 \cdot \cos(\theta) \cdot t \] \[ y = v_0 \cdot \sin(\theta) \cdot t - \frac{1}{2} \cdot g \cdot t^2 \]

Where:

\( x \) — Horizontal distance (meters)
\( y \) — Vertical distance (meters)
\( v_0 \) — Initial velocity (m/s)
\( \theta \) — Launch angle (degrees)
\( t \) — Time (seconds)
\( g \) — Gravitational acceleration (9.81 m/s²)

Explanation: The horizontal motion is constant velocity, while vertical motion is affected by gravity.

3. Importance of Projectile Calculations

Details: Understanding projectile motion is essential for ballistics, sports physics, engineering applications, and basic physics education.

4. Using the Calculator

Tips: Enter the initial velocity (m/s), launch angle (0-90°), and time (seconds). All values must be ≥ 0.

5. Frequently Asked Questions (FAQ)

Q1: What if I get a negative y value?
A: A negative y value means the projectile has descended below the initial launch height.

Q2: How do I calculate maximum height?
A: Maximum height occurs when vertical velocity becomes zero. Use \( t = v_0 \cdot \sin(\theta)/g \) in the y equation.

Q3: What about air resistance?
A: These equations ignore air resistance, which significantly affects real-world projectiles.

Q4: What's the range of valid angles?
A: Angles should be between 0° (horizontal) and 90° (vertical) for standard projectile motion.

Q5: Can I calculate time of flight?
A: Total flight time is \( 2 \cdot v_0 \cdot \sin(\theta)/g \) for level ground.