Initial velocity and angle when a ball is kicked over a 3m fence

[neilparker62]

This completes the condition for optimizing one of $\Delta x$, $\Delta y$ or $v_0$ as the projection angle is varied:

"At optimization,(a) the projection velocity and the velocity at target are perpendicular and (b) the transit time is the same as if the projectile were dropped from rest a distance equal to the magnitude of the overall displacement vector."

I am amazed that there is still juice left to squeeze out of projectile motion.

See also Winans Equations 20 - 27.

 

[kuruman]

Instead of being amazed I should have reread Winans. Nevertheless, I think it's good to bring forth this simple statement of trajectory optimization. It is more likely to be noticed here than in a 1961 AJP article.

 

[neilparker62]

Instead of being amazed I should have reread Winans. Nevertheless, I think it's good to bring forth this simple statement of trajectory optimization. It is more likely to be noticed here than in a 1961 AJP article.

It most definitely is. Not to mention $\vec{a}\times \vec{s} = \vec{v} \times \vec{u}$ which I 'punt' whenever I can!