1. What is Projectile Motion?

Projectile motion describes the motion of an object thrown or projected into the air, subject to gravity. The path followed by a projectile is called its trajectory, which is typically parabolic under constant gravity.

2. How Does the Calculator Work?

The calculator uses the projectile motion equations:

Where:

• \( v \) — Initial velocity (m/s)
• \( \theta \) — Launch angle (degrees)
• \( t \) — Time (seconds)
• \( g \) — Acceleration due to gravity (m/s²)
• \( x \) — Horizontal position (meters)
• \( y \) — Vertical position (meters)

Explanation: These equations calculate the position of a projectile at any given time, accounting for both horizontal motion (constant velocity) and vertical motion (accelerated motion under gravity).

3. Importance of Projectile Motion Calculation

Details: Understanding projectile motion is essential in physics, engineering, sports science, and various real-world applications such as ballistics, sports performance analysis, and trajectory planning.

4. Using the Calculator

Tips: Enter initial velocity in m/s, launch angle in degrees (0-90), time in seconds, and gravity in m/s² (default is 9.8 m/s²). All values must be positive.

5. Frequently Asked Questions (FAQ)

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

Q2: What is the range of a projectile?
A: The horizontal distance traveled: \( R = \frac{v^2 \sin(2\theta)}{g} \)

Q3: How does air resistance affect projectile motion?
A: Air resistance reduces both range and maximum height, making the trajectory asymmetrical and shorter than ideal calculations.

Q4: What is the time of flight?
A: Total time the projectile remains in air: \( T = \frac{2v \sin\theta}{g} \)

Q5: Can this calculator handle negative time values?
A: No, time must be positive as it represents the elapsed time since launch.