Study Guides/Physics/Motion in a Plane Class 11
Study Guide · Physics

Motion in a Plane — Class 11 Physics Notes

Chapter 4 of Class 11 Physics extends 1D motion to 2D. Motion in a plane requires vectors and covers key topics like projectile motion and uniform circular motion.

Question (Click to Flip)

At what angle is the projectile range maximum?

Answer

The horizontal range is maximum at θ = 45°. At this angle, sin2θ = sin90° = 1, giving R = u²/g (maximum possible range).

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Key Facts

In projectile motion, horizontal velocity remains constant (no air resistance), while vertical velocity changes due to gravity. These two components are completely independent.

Scalars and Vectors

  • Scalar: Has only magnitude. (e.g., speed, mass, temperature)
  • Vector: Has both magnitude and direction. (e.g., velocity, displacement, force)

Vector Addition — Triangle Law: If two vectors are placed head to tail, the resultant is the vector from the tail of the first to the head of the second.

Projectile Motion

When an object is thrown at an angle and moves under gravity alone — that is projectile motion.

Key formulas (initial velocity u at angle θ):

  • Time of flight: T = 2u sinθ / g
  • Maximum height: H = u²sin²θ / 2g
  • Horizontal range: R = u²sin2θ / g
  • Range is maximum at θ = 45°

Uniform Circular Motion

Motion in a circle with constant speed.

  • Direction changes continuously → acceleration exists (centripetal).
  • Centripetal acceleration: a = v²/r
  • Period: T = 2πr/v

Questions and Answers

At what angle is the projectile range maximum?+

The horizontal range is maximum at **θ = 45°**. At this angle, sin2θ = sin90° = 1, giving R = u²/g (maximum possible range).

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