1. What is the Final Velocity Equation?

The final velocity equation \( v = \sqrt{2 g h} \) calculates the speed of an object in free fall after falling from a certain height, assuming no air resistance. This equation is derived from the conservation of energy principle.

2. How Does the Calculator Work?

The calculator uses the final velocity equation:

Where:

• \( v \) — Final velocity (m/s)
• \( g \) — Acceleration due to gravity (m/s²)
• \( h \) — Height or distance fallen (m)

Explanation: The equation shows that the final velocity depends only on gravity and height, not on the mass of the object. This is a result of the equivalence principle in physics.

3. Importance of Final Velocity Calculation

Details: Calculating final velocity is essential in physics, engineering, and safety analysis. It helps determine impact forces, design safety systems, and understand motion in gravitational fields.

4. Using the Calculator

Tips: Enter gravity in m/s² (9.8 m/s² on Earth) and height in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why doesn't mass appear in the equation?
A: In free fall without air resistance, all objects accelerate at the same rate regardless of mass, so mass cancels out in the energy conservation equation.

Q2: What value should I use for gravity?
A: Use 9.8 m/s² for Earth's surface. For other planets or locations, use the appropriate gravitational acceleration.

Q3: Does this equation account for air resistance?
A: No, this is an idealized equation that assumes no air resistance. In reality, air resistance affects falling objects, especially at high velocities.

Q4: Can I use this for objects thrown upward?
A: This specific equation calculates velocity at impact after falling from rest. For objects with initial velocity, different equations apply.

Q5: What are typical final velocities?
A: From 10m height on Earth, final velocity is about 14 m/s (50 km/h). From 100m, it's about 44 m/s (158 km/h).