I would like to program a game based on an old physics problem. It is a combination of projectile motion and free fall. The problem: a hunter wants to shoot a monkey hanging on a tree branch. The monkeys are clever. The moment they see you fire, they let go of the tree. The problem: give an initial height of the monkey and the speed and angle of the projectile needed to hit the monkey. By allowing all three variables (only the horizontal distance to the tree is fixed) the player can get a real feel for projectile motion and free fall.
I will write it in TI-Basic on an 83+
docBill
P.S. This is my first contest, is there anything I have omitted

Welcome to Cemetech, Docbill! Be sure to Introduce Yourself when you get a chance. It sounds to me like your program plan will fit well into the contest rules. I think you mentioned everything you need to mention for starters, but make sure you keep your topic updated as you make progress, and be aware that the deadline is in fewer than three weeks!

But doesn't the hunter only have to aim right at the monkey, whatever the speed of the projectile is, if the monkey starts falling at the same moment the projectile is thrown ?

Or do you mean with "hanging" that the monkey has an horizontal movement which induces an initial velocity ? But then don't you "just" have to fire when the monkey is at an "edge" of its movement ?

Yeah, the solution to that problem is that you aim straight at the monkey and let fly with enough velocity to carry the projectile the horizontal distance to the tree. But I'm guessing there's more to your game than that?

Yeah, this is why I was asking if the monkey had an initial velocity. And the "enough velocity" for the projectile is basically "max velocity", since the result doesn't depend on the velocity. I think there should be wind, or obstacles (you have to choose the velocity wisely to avoid obstacles), or something, otherwise the game is going to be trivial.

It would only be trivial if the projectile and the monkey started at the same height, if I remember my physics correctly. If they started at dissimilar heights, I think it's not so trivial anymore. Hmm. I was starting to write out the counterexample to prove my point, and I realized that that was not in fact the case. I therefore think you would have to add things like the monkey letting go after being startled by the sound of the shot and so on. It would of course be a nice first phase to teach the user the interesting property we're discussing here, of course. Just be aware that you have only 2 weeks left, people!

Nope, I checked the property before posting here, and really, you just have to aim right at the monkey, whatever the speed of your projectile is. The two limits are when you have an infinite speed and the projectile instantly hits the monkey, and when you have a velocity of 0 and the projectile hits the monkey at the infinite (in other words, never).

So yeah, I think that some elements should be added, like wind or something. Or maybe gameplay elements such as rings that the user wants to collect before hitting the monkey, so the velocity of the projectile needs to be adjusted.

You do need to have enough velocity or the bullet hits the ground before reaching the monkey, but I will consider some additions

I took your advice and added 2 new features: 1) release on sight or sound. Sight is immediate while sound waits for the sound to reach the monkey. The delay depends on the distance to the monkey. 2) Added the capability to have a horizontal wind affect the projectile. With these two features, aiming is no longer trivial! Thanks to all, program has been submitted.
docbill
P.S. While I am aware of the byte saving techniques, the program is short enough that I went with style rather than saving some memory.

Those were both good solutions to the problem of trivial aiming. You say you submitted the program, but I didn't receive an email with your entry in the contest mailbox yet. Did you send it to contest@ this domain?

Yes, I sent it twice. The second time was zipped with the readme

Can you go to your sent mail and forward me the last e-mail of the program you sent? My e-mail is my username at gmail, I'll also PM it to you for a direct copy-paste.

I'm not promising the inclusion of your program but at least this way I can forward it to the judges.

Comic, we received his entry; it's in the zip of entries and rubrics I sent to all of the administrators.

Good to know! Thanks. I misread the date of your post.