How Can You Simplify Calculations for Artillery Projectile Motion?

[Philosophaie]

Given:
A fixed barrel velocity, $$v_{0}$$
An elevation of the piece of artilery, e
Target distance, x
Target elevation, te

Find:
time of travel, t
angle of the artilery, a

Equations:
$$y_{0}$$ = te - e

x = $$v_{0}$$ * cos(a) * t
y = $$y_{0}$$ + $$v_{0}$$ * sin(a) * t - 0.5 * g * $$t^{2}$$

If you try solving these for a and t, it gets ugly. Is there an equation I am missing or another way around this?

 

[Cyosis]

You're y_0 seems wrong. At t=0 the elevation should be e should it not? Other than that it looks good, two equations, two variables therefore solvable.

tip:put your entire equations between tex brackets it will look at a lot better.

 

[nlightner]

I would suggest using the quadratic formula to solve for t in the second equation, and then plugging that value into the first equation to solve for a. This will give you a value for the angle of the artillery and the time of travel. Alternatively, you could also use numerical methods or a computer program to solve for these values. It is also possible that there may be other equations or methods specific to projectile motion of artillery that could simplify the process. It would be beneficial to consult with experts in the field or conduct further research to find more efficient methods for solving this problem.