Danie Brink

THE RUGBY PROBLEM

In the sport of rugby, when a try (equivalent to a touchdown) is scored, the conversion kick has to be taken perpendicularly to where the try was scored. The distance that the kicker takes the ball back may vary. The kicker will be successful with the kick if he manages to kick the ball into the angle made by the two goalposts (angle CAB in the sketches below). The goal of a kicker, therefore has to be to find the maximum angle to the goalposts.

 Firstly, if he should take the ball back only a few meters (see point A), the angle to the goalposts (angle CAB) is small.

 Secondly, If he takes the ball back further (see point A), the angle (angle CAB) increases. But only up to a certain point! After a certain point, the angle to the goalposts decreases again.

 The goal of every kicker should be to optomize the angle in which he should kick. The following animation will assist a kicker to optomize the kicking angle. If you have Geometer's Sketchpad, you can click here or on the sketch alongside to see the animation. Bottom Line: Most kickers take the ball back too far. A general rule of thumb is to keep the distance to the nearest goalpost (CD on sketch) equal to the distance that you move the ball backwards (AD on sketch). If you score closer than 12 meters to one of the goalposts, take the ball back 12 meters (not to be charged down). From further than 12 meters from one of the goalposts, take it back equidistant from the post to the place the try was scored. I.e. CD = AD.   If this mathematical rule is applied, a kicker will only take the ball to the 22 meter line when the try is scored close to the touchline. To refine the process you can do the animation and find the optimal kicking place.

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