You kick a ball over a flat field. Taking into account gravity, but disregarding everything else like wind, friction, bounces, etc., etc., at what angle should you kick it so the ball lands the farthest away from you? And at what angle should you kick it so the ball makes the longest trajectory before landing?
(In reply to
Proof that the second part needs a numberical solution by ajosin)
The following program does work out
tan a = e^(1/sin a)  sec a
iteratively and comes out with a negative of the previously found value. It finds 56.46583512745234 degrees. Someone might explain why it comes out negative.
DEFDBL AZ
DIM SHARED pi, dr
pi = ATN(1) * 4
dr = pi / 180
a = 75
DO
aPrev = a
a = ATN(EXP(1 / SIN(a * dr))  1 / COS(a * dr)) / dr
PRINT a
LOOP UNTIL aPrev = a

Posted by Charlie
on 20050319 20:43:47 