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in my algebra-based course, I derive [eq 2] by combining the two component
equations:
Vf_x^2 = Vi_x^2 + 2a_x d_x
and
Vf_y^2 = Vi_y^2 + 2a_y d_y
to give
(Vf_x^2 + Vf_y^2) = (Vi_x^2 + Vi_y^2) + 2 (a_x d_x + a_y d_y)
which can then be written as
Vf^2 = Vi^2 + 2 (a dot d)
To me, this makes more sense since now it is more clear why work is defined
as the dot product (i.e., with the cosine of the angle). Since I don't see
this approach in the textbooks, I wonder if this is pedagogically or
physically correct.
That is my question - why isn't this approach used in textbooks?