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Motion in a Plane – Class 11 Physics NCERT | Projectile Motion, Vectors, Derivations & Formulas

🌍 Motion in a Plane – Class 11 Physics (NCERT)

Motion in a Plane deals with movement in two dimensions, using the concepts of vectors and projectile motion. This is the second part of kinematics after motion in a straight line.

📘 Key Concepts

  • Scalars: Quantities with magnitude only (e.g., speed, mass)
  • Vectors: Quantities with both magnitude and direction (e.g., velocity, displacement)
  • Vector Addition: Using triangle or parallelogram law
  • Resolution of Vectors: Splitting a vector into components along x and y axes

🧮 Basic Vector Formulas

  • Resultant of two vectors:
    R = √(A² + B² + 2ABcosθ)
  • Component form:
    A = Axî + Ayĵ
  • Magnitude:
    |A| = √(Ax² + Ay²)
  • Direction:
    θ = tan⁻¹(Ay/Ax)

🎯 Projectile Motion

When an object is thrown at an angle, it follows a curved path called a projectile. It is a 2D motion with horizontal and vertical components.

📌 Assumptions:

  • Acceleration due to gravity acts vertically downward
  • Horizontal velocity remains constant
  • Air resistance is neglected

🧾 Equations for Projectile Motion

Quantity Formula
Time of flight (T) T = (2u sinθ)/g
Maximum height (H) H = (u² sin²θ)/(2g)
Horizontal range (R) R = (u² sin2θ)/g

Component-wise Equations

Let initial velocity be u at angle θ with horizontal:

  • Horizontal velocity: ux = u cosθ
  • Vertical velocity: uy = u sinθ
  • Horizontal displacement: x = u cosθ × t
  • Vertical displacement: y = u sinθ × t – ½gt²

🔄 Circular Motion (Brief)

Circular motion is also motion in a plane, where the object moves in a circle of radius r.

  • Velocity direction changes continuously
  • Centripetal acceleration:
    ac = v²/r
  • Centripetal force:
    F = mv²/r

📋 Summary Table

Concept Formula
Resultant Vector R = √(A² + B² + 2ABcosθ)
Time of Flight T = (2u sinθ)/g
Max Height H = (u² sin²θ)/(2g)
Range R = (u² sin2θ)/g
Centripetal Acceleration a = v²/r

📝 Final Notes

  • Always resolve motion into x and y components
  • Use vector algebra for 2D analysis
  • Projectile motion is symmetrical (if on level ground)

Tags: Motion in a Plane, Class 11 Physics, NCERT Kinematics, Vectors and Projectile, Physics Notes, Science Blog, CBSE Physics, JEE NEET Prep

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