Question

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 theta is the rock thrown?

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

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

Answer 1

I understand everything up until where you go from sin^2theta/2 = 2sin theta cos theta. Where does tan theta = 4 after that come form??

Answer 2

If R = H,
Then u^2 sin^2 θ / (2 g) = 2u^2 sin θ cos θ / g.
Therefore sin θ / cos θ = tan θ = 4.
Thus θ = arctan (4) = 75.96... degrees.