It’s been a busy day and I haven’t the energy for anything strenuous so I thought I’d put up a cute problem I was thinking about (for some reason) on the train home from Friday’s concert.
You may have to refresh your memory about units as well as the geometry of ellipses. The following picture will help:
According to Kepler’s First Law of Cricket, the boundary of a cricket field is in the shape of an ellipse, with the two middle stumps each marking one of the foci. These are 22 yards apart, defining the length of the pitch P. The distance from one middle stump to the square leg or cover point boundary is 65 yards. This distance, called S, is the semi-latus rectum of the ellipse.
- Derive a formula connecting the eccentricity e of the ellipse to P and S and calculate the value of e for the given values of S and P.
- Calculate the major and minor axes of the ellipse for the given value of S.
- Calculate the maximum distance from the stumps to the boundary for the given value of S.
- Calculate the area of the playing surface in acres for the given value of S.
The value of S given above is the minimum allowed for First-class Cricket. The maximum is 90 yards. Repeat Qs 2-4 for this value of S. (P is always fixed at 22 yds.)
