1. What is Horizontal Velocity?

Horizontal velocity (v_x) is the constant velocity component parallel to the ground in projectile motion. It remains unchanged throughout the flight (ignoring air resistance) as there is no horizontal acceleration.

2. How Does the Calculator Work?

The calculator uses the horizontal velocity equation:

Where:

• \( v \) — Initial velocity (m/s)
• \( \theta \) — Angle of elevation (degrees)
• \( v_x \) — Horizontal velocity component (m/s)

Explanation: The equation calculates the horizontal component of velocity by multiplying the initial velocity by the cosine of the launch angle.

3. Importance of Horizontal Velocity Calculation

Details: Horizontal velocity is crucial for determining the range of projectile motion, time of flight, and analyzing motion in two dimensions. It's fundamental in physics, engineering, and ballistics.

4. Using the Calculator

Tips: Enter initial velocity in m/s and angle in degrees (0-90). All values must be valid (velocity > 0, angle between 0-90 degrees).

5. Frequently Asked Questions (FAQ)

Q1: Why does horizontal velocity remain constant?
A: In ideal projectile motion (no air resistance), there's no horizontal acceleration, so the horizontal component of velocity remains unchanged.

Q2: What happens at 0 degrees elevation?
A: At 0° (horizontal launch), v_x = v since cos(0°) = 1. All initial velocity is horizontal.

Q3: What happens at 90 degrees elevation?
A: At 90° (vertical launch), v_x = 0 since cos(90°) = 0. There is no horizontal component.

Q4: How does air resistance affect horizontal velocity?
A: In reality, air resistance causes horizontal velocity to decrease over time, making the actual range shorter than theoretical calculations.

Q5: What's the relationship between angle and horizontal velocity?
A: For a given initial velocity, horizontal velocity decreases as the angle increases from 0° to 90° following the cosine function.