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Projectile Motion

From basics to real-world applications

What is Projectile Motion?

Projectile motion is the curved path an object follows when it is thrown or launched near the Earth's surface. It combines horizontal motion (constant speed) with vertical motion (affected by gravity).

Initial Velocity (v₀)

The speed at which the object is launched, in m/s or ft/s.

Angle of Projection (θ)

The angle above horizontal at which the object is launched.

Gravity (g)

Acceleration due to gravity — 9.81 m/s² on Earth.

Time of Flight (T)

Total time the object spends in the air before landing.

Key Formulas

Horizontal Range

R = (v² × sin(2θ)) / g

Maximum Height

H = (v² × sin²(θ)) / (2g)

Time of Flight

T = (2v × sin(θ)) / g

Example Problem

  • Initial velocity: 50 m/s
  • Angle: 45°
  • Gravity: 9.81 m/s²

Range ≈ 255 m · Max Height ≈ 63.8 m · Time ≈ 7.2 s

Real-Life Examples

  • A football being kicked across the field
  • Water from a garden hose arcing through the air
  • A basketball shot towards the hoop
  • Artillery shells and missile trajectories in engineering
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