Hello Eleven ElevenIn the attached diagram:is the distance to the left of the left-hand post where the try was scored.Then we need to make a couple of assumptions about the nature of the kick at goal:

is the distance apart of the posts.

is the distance back from the goal-line from which the kick is taken.

For very small values of and it will not be possible for the kicker to achieve the elevation required to clear the bar. So we'll assume that for the values we shall consider, and/or are large enough for this not to be a problem.Therefore we shall concern ourselves only with the angle subtended by the posts at the point from which the kick is taken (the angle in the diagram): the greater the angle , the greater the chance that the kick is successful.

We'll also assume that as and become larger, the directional accuracy of the kick remains constant. (In practice this is not necessarily the case: a kick taken from the half-way line requires considerably more energy than one from the 22 metre line, and therefore may be subject to a greater degree of error in its direction.)

In the diagram, then:At this stage, we have a choice about how to find the value of that gives the maximum value of . If you are allowed to use graphical methods, it is very easy to put some values into a spreadsheet to produce a graph. If you have Excel, you can open the attached spreadsheet file. If not, I've extracted the graph.

For and , the optimum value of is around metres.

If you're not allowed to use a graphical method, I have a calculus method which gives the value of as , giving as the answer.

I'll post this solution for you if you'd like to see it.

As far as the final part of the question is concerned, this is pretty open ended. In the diagram the angle subtended from a point directly in front of the posts is , whereYou could work out some values of and for various values of and . (If the kick is on the touchline, will be around metres, depending on the width of the pitch.) Then if, for certain values, , for example, you could say that it was twice as difficult from the touchline than from under the posts.

Grandad