Originally Posted by

**shilz222** A boy stands at the peak of a hill which slopes downward uniformly at angle $\displaystyle \phi $. At what angle $\displaystyle \theta $ from the horizontal should he throw a rock so that is has the greatest range.

Ok, so this is a rotation of the normal $\displaystyle x_{1} - x_{2} $ plane right? So we can use the direction cosines $\displaystyle \lambda_{ij} $ to make this problem easier.

So $\displaystyle x'_{1} = x_{1} \cos \phi + x_{2} \cos \left(\frac{\pi}{2} + \phi \right) $ and $\displaystyle x'_{2} = \cos \theta + \cos \phi $.

Are these the right transformations? Is this the right way to set up the problem?