Question

(I'm a video game developer) I am programming realistic physics, how do I determine the firing angle for the archer to hit its target if the archer and the target are on uneven ground?

Answer 1

You can break the motion of an object shut up at an angle by breaking the initial velocity into x and y components.
\(\sf \color{red}{v_{xi} = v_i~cos(\theta)}\) and \(\sf \color{blue}{v_{yi} = v_i~sin(\theta)}\)

Answer 2

Since the veolcty components are independent, and gravity only acts in the \(y\) direction (on an xy-coordinate, obviously), that means that \(v_x\) position is constant. Which means that you can use: \(\sf \color{green}{v_y = v_{yi}+gt}\), where \(\sf \color{green}{v_{yi}}\) = \(\sf \color{blue}{v_i~sin(\theta)}\)

as you know, \(g\) = gravity = \(\sf \color{}{9.8 \frac{m}{s^2}}\)

Answer 3

Since gravity does not affect the \(\sf \color{}{v_{xi} }\) there is no need to include difference of gravity.

Answer 4

If you want to know the positions of the cannon ball at any position, you can use either or.

Answer 5

this is of course, ignoring air resistance, as you would be using a slightly different approach with higher math.

Answer 6

This article does a nice job deriving a "general" equation for the range of a projectile. The general case includes height differentials. http://en.wikipedia.org/wiki/Range_of_a_projectile

Answer 7

So what would be the calculation for hitting a target up or down a hill?

Answer 8

Well, that depends on the values that you're using! Duh!

Answer 9

Well, I mean I see the calculation on Wiki, but how would one solve for theta(the angle)?

Answer 10

That calculation is not working out. What I'm doing is firing up or down a hill, thats the calculation I'm trying to find, and Thank You In Advance!!!!