Throw the ball. Watch the parabola build the formula for you.
This is projectile motion — the chapter that scares people with "range" and "time of flight" formulas. Change the angle and speed below and watch what actually happens first.
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Range (m)
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Max height (m)
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Time (s)
Notice: 45° always goes the farthest for a given speed. That single observation is the "maximum range at 45°" fact your book states — you just watched why.