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Introduction

In a previous Physics Forums article entitled “How to Master Projectile Motion Without Quadratics”, PF user @kuruman brought to our attention the vector equation ##\frac{|V_0 \times V_f|}{g} = R## and lamented the fact that:

“Equally unused, untaught and apparently not even assigned as a “show that” exercise is Equation (4) that identifies the range as the magnitude of the cross product of the initial and final velocity divided by g.”

In this article, we reproduce and make use of equations presented in a 60s vintage article from the American Journal of Physics entitled “Convenient Equations for Projectile Motion”. The article abstract indicates:

“Quaternion multiplication of the basic vector equations for uniformly...

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