CLS-32

Projectile range

Flat-earth vacuum range.

Reading speed

GoverningProjectile range

Governing equation

R=v^2\sin 2\theta/g

where

v: v (m/s)
th: th (deg)
R: Projectile range (m)

Lecture brief

Historical brief

Newtonian mechanics (1687) plus energy, angular momentum, Kepler and the ballistic parabola remain the first language of motion. Every sheet here is a closed-form orbit, throw, spin or oscillator. This sheet (CLS-32 — Projectile range) is the form associated with Projectile range. Working symbols: $v$ , $th$ $\rightarrow$ $R$ . Flat-earth vacuum range. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

R

from

v

th

in Classical mechanics via

R=v^2\sin 2\theta/g

Flat-earth vacuum range. Use it when a real classical mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

v = 40.000\,\mathrm{m/s}

th = 35.000\,\mathrm{deg}

, the governing relation

R=v^2\sin 2\theta/g

yields

R = 153.263\,\mathrm{m}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

v v40 m/sth th35 deg

Outputs

Projectile range R153.263 m

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Flat-earth vacuum range. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube