Chapter 6.3, Problem 58E

To determine

(a)

To find:

Using the result from Regiomontanus’ problem when the line is outside the goalposts, the optimal location to kick the rugby ball lies on the following hyperbola.

$x^2-y^2={9.25}^2$

To determine

(b)

To find:

If the line on which the ball must be kicked is $10$ ft to the right of the goalpost, how far from the goal line should the ball be placed to maximize angle $\theta$.

To determine

(c)

To find:

Rugby players find it easier to kick the ball from the hyperbola’s asymptote. When the line on which the ball must be kicked is $10$ ft to the right of the goalpost, how far will this point differ from the exact optimal location.