1. What is the Trajectory Formula?

The trajectory equations describe the motion of a projectile under the influence of gravity. They calculate the horizontal (x) and vertical (y) positions of the projectile at any given time (t).

2. How Does the Calculator Work?

The calculator uses the trajectory equations:

Where:

• \( v \) — Initial velocity (m/s)
• \( \theta \) — Launch angle (degrees)
• \( t \) — Time (seconds)
• \( g \) — Acceleration due to gravity (9.81 m/s² on Earth)

Explanation: The equations account for both the horizontal motion (constant velocity) and vertical motion (accelerated motion under gravity).

3. Importance of Trajectory Calculation

Details: Trajectory calculations are essential in physics, engineering, ballistics, sports science, and many other fields where projectile motion needs to be predicted.

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 (9.81 for Earth). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What assumptions does this formula make?
A: It assumes no air resistance, uniform gravity, flat ground, and that the launch and landing heights are equal.

Q2: How do I calculate maximum height?
A: Maximum height occurs when vertical velocity becomes zero. Use \( t = v\sinθ/g \) in the y equation.

Q3: How do I calculate range?
A: Range is the x position when y returns to zero (total flight time is \( 2v\sinθ/g \)).

Q4: What's the optimal angle for maximum range?
A: 45 degrees gives maximum range when launch and landing heights are equal.

Q5: Can this be used for non-horizontal launches?
A: Yes, but the equations assume the launch angle is measured from horizontal.