## Kinematics

*The branch of mechanics concerned with the motion of objects without reference to the forces that cause the motion.*

How do Kinematics relate to rugby?

Kinematics in general, is the study of mechanics which

*describes the motion of objects and systems without consideration of the causes of motion*. Concepts of Kinematics can be seen and explored all over the rugby field, and are used to help explain the physics behind things such as the motion of a ball through the air during a pass, or even the acceleration and velocity of a forward in motion.

Passing

In rugby, to get the ball to a teammate as fast as possible, passing extremely low and quick is key. During a spin pass, the passer will throw the ball at no more than a 15 degree angle (which is only for an extremely long pass) to get the ball to his teammate.

## A pass

For example, Dan Carter of the All Blacks can throw the ball at 20m/s at an angle of 15 degrees, and using this info we can draw the horizontal and vertical components and find their speeds using trigonometry laws.

## Vertical

To the right we have the vertical component, to find the total time it takes to reach maximum height the only thing we need is the initial velocity. Acceleration is the acceleration due to gravity which is -9.8 m/s/s. And the speed right when it reaches max height is also known, 0m/s because it is motionless for an instant.

## horizontal

By splitting the vector into 2 components, we can now found out many other things including max height, time to reach max height, total time to reach the target and total horizontal displacement.

## Result!

Assuming the ball is thrown and caught at hip level (1m) we can find out everything about the flight using the info we gained above. We can find the max height it reaches, the time it takes to reach the max and the target, and the rest of the data from the start, to the max, and until the catch.

- Vv = Vertical Velocity
- Vh = Horizontal Velocity
- a = Acceleration
- dv = Vertical Displacement
- dh = Horizontal Displacement
- t = Time