1. What is Projectile Motion?

Projectile motion refers to the motion of an object projected into the air and moving under the influence of gravity. It follows a parabolic trajectory and can be analyzed by separating the motion into horizontal and vertical components.

2. How Does the Calculator Work?

The calculator uses the projectile motion equations:

Where:

• \( V_x \) — Horizontal velocity component (m/s)
• \( V_y \) — Vertical velocity component (m/s)
• \( V \) — Initial velocity (m/s)
• \( \theta \) — Launch angle (degrees)
• \( g \) — Acceleration due to gravity (9.81 m/s²)
• \( t \) — Time (seconds)

Explanation: The horizontal velocity remains constant (ignoring air resistance), while the vertical velocity changes due to gravitational acceleration.

3. Importance of Projectile Motion Calculations

Details: Understanding projectile motion is essential in physics, engineering, sports science, and military applications. It helps predict the trajectory, range, and maximum height of projectiles.

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. All values must be positive and within valid ranges.

5. Frequently Asked Questions (FAQ)

Q1: Why does horizontal velocity remain constant?
A: In ideal projectile motion (ignoring air resistance), there are no horizontal forces acting on the object, so horizontal velocity remains constant.

Q2: What is the maximum height of a projectile?
A: Maximum height occurs when vertical velocity becomes zero: \( h_{max} = \frac{(V \cdot \sin(\theta))^2}{2g} \)

Q3: How do you calculate the range of a projectile?
A: Range is calculated as: \( R = \frac{V^2 \cdot \sin(2\theta)}{g} \)

Q4: What assumptions are made in these calculations?
A: The calculations assume no air resistance, uniform gravitational field, and flat Earth surface.

Q5: Can this calculator handle negative time values?
A: No, time must be a positive value representing the elapsed time since launch.