Projectile motion, simultaneous equations, arbitrary values,

in /by

Projectile motion, simultaneous equations, arbitrary values,

From
Physics for Scientists and Engineers, 6th Edition 6th Edition by Paul A. Tipler (Author), Gene Mosca (Author)https://gyazo.com/5c59508ac1591d40ece62ab248ae37b2
Example 3-10: The Ranger and the Monkey, part Ahttps://gyazo.com/959989443146fba7739df09c06a18bd0
I do not find the book’s answer satisfactory as they do not strictly show mathematically how the equations to produce the end co-ordinates are equivalent with arbitrary values.
i.e. I feel like they are making assumptions that are not shown mathematically and I would like to know how to express the entire answer mathematically in the form “equation 1 = equation 2”
Any advice specifically or in terms of an approach would be welcomed

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