Complementary Angles in Projectile Motion Explained with Example (θ₁ + θ₂ = 90°)

Описание: In projectile motion, two angles of projection are called complementary if their sum is 90°.
For the same initial velocity, both projectiles cover the same horizontal range, but have different heights and times of flight.


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🧠 Stepwise Explanation with Example:

1️⃣ Given:
Let a body be projected with the same initial speed at two angles and .
If , then these are called complementary angles.

2️⃣ Formula for Range:

R = \frac{u^2 \sin 2\theta}{g}

3️⃣ For complementary angles:

2\theta_1 + 2\theta_2 = 180° \Rightarrow \sin(2\theta_1) = \sin(2\theta_2)

4️⃣ Numerical Example:
Let ,

For :


R_1 = \frac{u^2 \sin 60°}{g} = \frac{400 \times 0.866}{10} = 34.64 \, m

R_2 = \frac{u^2 \sin 120°}{g} = \frac{400 \times 0.866}{10} = 34.64 \, m

✅ Thus, R₁ = R₂ = 34.64 m

However:

Maximum Height (H) and Time of Flight (T) are different.








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✅ Final Concept Summary:

Complementary Angles → θ₁ + θ₂ = 90°

Same Range for same u

Higher angle → Greater height & time

Lower angle → Lesser height, same range



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📍 Timestamps:
00:00 – Introduction
00:25 – Complementary Angles Concept
01:40 – Derivation using Range Formula
03:00 – Numerical Example
04:20 – Summary & Key Results

⏱ Video Duration: 4.53 min


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