Q4E Case Study 17 – Relative Velocity

Proposed Subject usage:

Mathematics / Physics (A/AS level), Sports Science (Degree Yr 1/2)

Introduction

Relative velocity is generally associated with an object moving through a fluid – a fluid being defined as any substance that tends to flow or continuously deform when acted on by a shear force. However, relative velocity can also be calculated between two bodies. The relative velocity of a body is the velocity as it approaches or recedes another body, where one or both of the bodies are in motion. As velocity is a vector quantity, it is both magnitude and direction sensitive. The sign attached to the relative velocity indicates the direction of the relative velocity with respect to reference direction. Relative velocity refers to two moving bodies; it is not just the difference in the velocities.

Magnitude of the relative velocity of bodies moving in opposite directions to each other, i.e. moving closer together q or further apart q, is calculated as the algebraic sum of the speeds of the two bodies, remembering that they are direction aware and that in this case at least one of the values is travelling in a negative direction. Magnitude of the relative velocity of bodies moving in the same direction q is the difference in the speeds of body A and body B. If two bodies are moving in the same direction at the same velocity, then the relative velocity will be zero.

The equation for relative velocity is as follows:

VAB = VA – VB

Where:

VAB = is the velocity of body A as observed by body B

VA = velocity of body A

VB = velocity of body B

(alternatively, this can be switched around to find VBA, which is the velocity of body B relative to body A. This will result in the same value as VAB but in the opposite direction).

Objectives

To define relative velocity with reference to sports specific situations using the Quintic software

To calculate the relative velocity of two bodies during a rugby tackle.

Methods

The videos have been digitised and calibrated using the Quintic software.

A butterworth filter was used to smooth the data.

The video has been digitised and calibrated using the Quintic software.

Data has been exported to an excel file where it was used to calculate the velocity of the two bodies during the rugby tackle. Graphs have been prepared using this information.

Still images have been captured from videos to outline different stages of the exercise

Functions of the Quintic Software used:

One-Point Digitisation Module

Butterworth Filter

Calibration

Interactive Graph and Data displays

Export Data

Multi-Image Capture

Results