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 A-Z
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 2005-03-19 20:43:47