1. What is the Vertical Trajectory Equation?

The vertical trajectory equation calculates the position of an object in vertical motion at a given time, considering initial velocity and gravity. It's fundamental in physics for analyzing projectile motion.

2. How Does the Calculator Work?

The calculator uses the vertical trajectory equation:

Where:

• \( y \) — Vertical position (m)
• \( v_0 \) — Initial velocity (m/s)
• \( t \) — Time (s)
• \( g \) — Acceleration due to gravity (9.81 m/s² on Earth)

Explanation: The equation accounts for both the initial upward motion (first term) and the downward acceleration due to gravity (second term).

3. Importance of Vertical Trajectory Calculation

Details: Calculating vertical position is crucial for understanding projectile motion, designing trajectories in engineering applications, and solving physics problems involving free-fall or vertical launches.

4. Using the Calculator

Tips: Enter initial velocity in m/s, time in seconds, and gravity in m/s² (default is Earth's gravity 9.81 m/s²). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What does a negative y value mean?
A: A negative y value indicates the object is below the launch point (assuming y=0 at launch).

Q2: How does air resistance affect the calculation?
A: This equation ignores air resistance. For objects with significant air resistance, more complex models are needed.

Q3: Can this be used for horizontal motion?
A: No, this is specifically for vertical motion. Horizontal motion typically has constant velocity (no acceleration).

Q4: What's the maximum height reached?
A: Maximum height occurs when vertical velocity becomes zero: \( t = v_0/g \). Plug this time back into the equation to find maximum height.

Q5: How does changing gravity affect the results?
A: Lower gravity (e.g., on Moon) would result in higher trajectories and longer flight times for the same initial velocity.