If you can throw a ball vertically upward to a height h = 30.1 m, what is the maximum horizontal range over which you can throw the same ball, assuming you throw it at the same initial speed

Answer 1

Twice as far.
Here's the reason
The maximum height when you throw vertically is V^2/2g.
(That is easily proven using conservation of energy)
The RANGE X at any angle A is
2 sinAcosA/V^2/g, and the maximum range is obtainec at a A = 45 degree angle, for which
Xmax = V^2/g