Projectiles Topic Review summary

Key learning points

• Horizontal: $x=(u\\cos\\theta)t$; vertical: $y=(u\\sin\\theta)t-\\frac12 gt^2$.
• Time of flight, range, and max height formulae for level ground.
• Eliminate $t$ for the Cartesian trajectory equation.
• Greatest range on level ground at 45^\\circ (constant $u$).
• Speed at a point: combine velocity components with Pythagoras.

Worked example 1 — Range

Level range formula.

Working

Max when $\\sin2\\theta=1$.

Worked example 2 — Height

Max height.

Working

Vertical velocity zero at top.

Worked example 3 — Horizontal: x=(u\\\\cos\\\\theta)t; vertic

Horizontal: $x=(u\\\\cos\\\\theta)t$; vertical: $y=(u\\\\sin\\\\theta)t-\\\\frac12 gt^2$.

Working

Attempt without notes, then check the answers PDF.

Worked example 4 — Time of flight, range, and max height form

Apply this idea from the Topic Review: Time of flight, range, and max height formulae for level ground.

Working

Attempt without notes, then check the answers PDF.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.