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 Where am I wrong? by Larry)

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"Part 2:  Trajectory S = integral {t=0 to t(final)} ds
where ds^2 = dx^2 + dy^2
dx= V cosB dt
dy= [V sinB - gt] dt

(ds/dt)^2= V^2 (cosB)^2 + V^2 (sinB)^2 +(gt)^2 - 2Vg sinB t
          + 2 V^2 sinB cosB - 2Vg cosB t"


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Where do the last two terms come from?. Remember you want dx^2+dy^2, not (dx+dy)^2. I think it should be,

(ds/dt)^2= V^2 (cosB)^2 + V^2 (sinB)^2 +(gt)^2 - 2Vg sinB t

From here and after a couple of steps you will get to something that looks like,

s = integral{sqrt(z^2+1^2)dz}

Which can be done with the change of variable z = tan u. This is a beautifull problem worth some work, good luck.

Posted by ajosin on 2005-03-20 04:17:37