Max Range of Projectile on Non-Level Ground

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To derive the maximum range of a projectile on non-level ground, one must substitute the equations for vertical and horizontal components into the parabolic equation. The discussion emphasizes the importance of sharing any attempts made to identify specific errors in the approach. Suggestions include analyzing the turning point of the function, which occurs where the derivative equals zero. The conversation highlights the need for a clear understanding of the projectile's motion equations. Ultimately, deriving the correct equation requires careful consideration of the projectile's trajectory in relation to the ground's slope.
tman1
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My question is, derive an equation to find the maximum range of a projectile that's not on level ground. I am lost and i did attempt this, by making a diagram and subbing in what i thought i would need to use, but i still have not come up with the answer. please help
 
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tman1 said:
My question is, derive an equation to find the maximum range of a projectile that's not on level ground. I am lost and i did attempt this, by making a diagram and subbing in what i thought i would need to use, but i still have not come up with the answer. please help
I think the best thing you can do is post whatever you have done. I could suggest a lot but I don't know what is making you go wrong.

The Bob (2004 ©)
 
Substitute
y=R\ sin\alpha
and
x=R\ cos\alpha
in the parabolic equation for the projectile.
The range will then be a function of \theta.The turning point of a function occurs where the derivative is zero...
 
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