1. What is Projectile Motion?

Projectile motion refers to the motion of an object thrown or projected into the air, subject only to acceleration due to gravity. The initial velocity is crucial in determining the trajectory and range of the projectile.

2. How Does the Calculator Work?

The calculator uses the projectile motion equation:

Where:

• \( v_0 \) — Initial velocity (m/s)
• \( R \) — Range or horizontal distance (m)
• \( g \) — Acceleration due to gravity (9.81 m/s² on Earth)
• \( \theta \) — Launch angle (degrees)

Explanation: This equation calculates the initial velocity needed to achieve a certain range when launched at a specific angle, neglecting air resistance.

3. Importance of Initial Velocity

Details: Initial velocity is fundamental in projectile motion as it determines how far and how high the projectile will go. It's essential in fields like physics, engineering, ballistics, and sports science.

4. Using the Calculator

Tips: Enter the desired range in meters, launch angle in degrees (between 0 and 90), and acceleration due to gravity (9.81 m/s² for Earth). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What's the optimal angle for maximum range?
A: The maximum range is achieved at a 45° launch angle when air resistance is neglected.

Q2: Does this calculator account for air resistance?
A: No, this is the simplified version without air resistance. Real-world calculations may need additional factors.

Q3: What if I get an "undefined" result?
A: This happens at 0° or 90° angles where sin(2θ) equals zero, making division impossible. These angles don't produce horizontal motion.

Q4: Can I use this for other planets?
A: Yes, just change the gravity value to match the celestial body you're calculating for.

Q5: How accurate is this calculator?
A: It's theoretically accurate for ideal projectile motion without air resistance or other external forces.