This problem mentions that the rock is thrown on level ground, implying that it lands at the same height. Thus, it's a symmetrical launch problem.

For symmetrical launch:

Range:

$\overline{){\mathit{R}}{\mathbf{=}}\frac{{{\mathit{v}}_{\mathbf{0}}}^{\mathbf{2}}\mathbf{}\mathbf{sin}\mathbf{\left(}\mathbf{2}\mathit{\theta}\mathbf{\right)}}{\mathit{g}}}$

Maximum Height:

$\overline{){{\mathit{H}}}_{\mathit{m}\mathit{a}\mathit{x}}{\mathbf{=}}\frac{{{\mathit{v}}_{\mathbf{0}}}^{\mathbf{2}}\mathbf{}{\mathbf{sin}}^{\mathbf{2}}\mathit{\theta}}{\mathbf{2}\mathit{g}}}$

A rock is thrown upward from level ground in such a way that the maximum height of its flight is equal to its horizontal range R.

(a) At what angle θ is the rock thrown?

(b) In terms of its original range R what is the range Rmax the rock can attain if it is launched at the same speed but at the optimal angle for maximum range?

(c) What If? Would your answer to part (a) be different if the rock is thrown with the same speed on a different planet? Explain.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Special Equations in Symmetrical Launches concept. You can view video lessons to learn Special Equations in Symmetrical Launches. Or if you need more Special Equations in Symmetrical Launches practice, you can also practice Special Equations in Symmetrical Launches practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Efthimiou's class at UCF.