Formula to Calculate Horizontal Distance

Horizontal Distance Formula:

\[ R = \frac{v_0^2 \times \sin(2\theta)}{g} \]

Horizontal Distance (m):

1. What is the Horizontal Distance Calculator?

Definition: This calculator computes the horizontal distance traveled by a projectile based on its initial velocity and launch angle.

Purpose: It helps in physics, engineering, and ballistics to predict where a projectile will land.

2. How Does the Calculator Work?

The calculator uses the projectile motion formula:

\[ R = \frac{v_0^2 \times \sin(2\theta)}{g} \]

Where:

\( R \) — Horizontal distance (meters)
\( v_0 \) — Initial velocity (meters/second)
\( \theta \) — Launch angle (degrees)
\( g \) — Gravitational acceleration (9.8 m/s²)

Explanation: The formula calculates the range of a projectile launched from ground level, neglecting air resistance.

3. Importance of Horizontal Distance Calculation

Details: Accurate range prediction is crucial for applications like sports, military targeting, and physics experiments.

4. Using the Calculator

Tips: Enter the initial velocity in m/s and launch angle in degrees (0-90). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What angle gives maximum distance?
A: 45 degrees provides the maximum horizontal distance when launched from ground level.

Q2: Does this account for air resistance?
A: No, this is the idealized case without air resistance for simpler calculations.

Q3: What if my projectile starts from a height?
A: This formula is for ground-level launches. Different formulas are needed for elevated launches.

Q4: Why is gravitational acceleration 9.8 m/s²?
A: This is the standard value for Earth's gravity at sea level.

Q5: Can I use this for any projectile?
A: Yes, as long as air resistance is negligible and it's launched from ground level.