Enter the acceleration due to gravity and the height into the calculator to determine the theoretical velocity.

Theoretical Velocity Formula

The following equation is used to calculate the Theoretical Velocity.

TV = SQRT ( 2*g*H)
  • Where TV is the theoretical velocity (m/s)
  • g is the acceleration due to gravity (m/s^2)
  • H is the height (m)

To calculate the theoretical velocity, take the square root of 2 times the acceleration due to gravity times the height.

What is a Theoretical Velocity?

Definition:

A theoretical velocity describes the maximum speed an object falling from a given height would reach if there was no air resistance.

How to Calculate Theoretical Velocity?

Example Problem:

The following example outlines the steps and information needed to calculate Theoretical Velocity.

First, determine the acceleration due to gravity. This is equal to 9.81 m/s^2.

Next, determine the height. For this problem, the height is found to be 30m.

Finally, calculate the Theoretical Velocity using the formula above:

TV = SQRT ( 2*g*H)

TV = SQRT ( 2*9.81*30)

TV = 24.26 m/s

FAQ

What factors can affect the accuracy of the theoretical velocity calculation?

The accuracy of the theoretical velocity calculation can be affected by factors such as air resistance, which is not considered in the basic formula, and inaccuracies in the measurements of height or the value used for the acceleration due to gravity, which can vary slightly depending on geographical location.

Can the theoretical velocity formula be used for objects thrown upwards or horizontally?

The theoretical velocity formula given (TV = SQRT(2*g*H)) is specifically for objects falling freely under gravity from a certain height. For objects thrown upwards or horizontally, additional factors such as initial velocity and angle of projection need to be considered, and different formulas would apply.

How does the acceleration due to gravity vary with location on Earth, and does it significantly impact the theoretical velocity calculation?

The acceleration due to gravity varies slightly across different locations on Earth, primarily due to differences in altitude and the Earth’s slightly oblate shape. This variation can affect the theoretical velocity calculation, but for most practical purposes, the standard value of 9.81 m/s^2 is sufficiently accurate. However, for precise scientific calculations, the specific local value of gravity should be used.