Introduction

The two flavours of projectile motion studied in this unit -- horizontal projection and angular (oblique) projection -- are both built from exactly the same two ingredients: unchanging horizontal velocity, and vertically accelerated motion under gravity, applied along perpendicular axes and then recombined.

In horizontal projection, the object is launched with a purely horizontal initial velocity $u$ from some height, and gravity alone curves its path downward as it travels forward -- the classic 'ball rolling off a table' scenario. In angular (oblique) projection, the object is launched at an angle $\theta$ to the horizontal with initial speed $u$, so it has both a horizontal component $u\cos\theta$ (constant throughout the flight, since gravity acts only vertically) and a vertical component $u\sin\theta$ (which decreases, reverses, then increases in magnitude under $-g$) -- the classic 'thrown ball' or 'fired projectile' scenario, whose path is a parabola. Both cases are solved by treating the horizontal and vertical motions as …