Projectile motion: path, height and rangeप्रक्षेप्य गति: पथ, ऊँचाई और परास

NCERT Fig 3.16 & 3.17 · interactive diagram

Parts and their functions

• Parabolic trajectory (परवलयिक प्रक्षेप-पथ) — y = (tan θ₀) x − g x² / (2 v₀² cos²θ₀): a parabola.
• Initial velocity v₀ (प्रारंभिक वेग v₀) — Launched at angle θ₀ above the horizontal.
• Components of v₀ (v₀ के घटक) — Horizontal v₀ cos θ₀ stays constant (aₓ = 0); vertical v₀ sin θ₀ changes (a_y = −g).
• Angle of projection θ₀ (प्रक्षेपण कोण θ₀) — Range is maximum at θ₀ = 45°: R_max = v₀²/g. θ₀ and 90° − θ₀ give the same range.
• Highest point (उच्चतम बिंदु) — Vertical velocity is zero; the body still moves horizontally. Reached at t_m = v₀ sin θ₀ / g.
• Maximum height H (अधिकतम ऊँचाई H) — H = (v₀ sin θ₀)² / 2g.
• Horizontal range R (क्षैतिज परास R) — R = v₀² sin 2θ₀ / g, covered in the time of flight T = 2v₀ sin θ₀ / g.
• Acceleration g (त्वरण g) — Always vertically down, the same at every point (air resistance neglected).

Original diagram drawn by Simple Learning Hub, based on NCERT Fig 3.16 & 3.17. Report a mistake