Topic 7: One-Page Revision Sheet

Chapter 4: Motion in a Plane – One Page Revision

1. Motion in a Plane

Motion involving two perpendicular directions is called two-dimensional motion or motion in a plane.

Examples

• Projectile motion
• Car taking a turn
• Bird flying in air

2. Scalars and Vectors

Scalars have only magnitude, while vectors have both magnitude and direction.

Examples

• Scalars: mass, time, speed, distance, energy
• Vectors: displacement, velocity, acceleration, force

3. Vector Addition

The combined effect of two or more vectors is represented by a single vector called the resultant.

Triangle Law

If two vectors are represented by two sides of a triangle taken in order, the third side taken in opposite order represents the resultant.

Parallelogram Law

If two vectors acting at a point are represented by adjacent sides of a parallelogram, the diagonal represents the resultant.

Resultant Magnitude

R = √(A² + B² + 2AB cosθ)

Special Cases

• θ = 0° → R = A + B
• θ = 90° → R = √(A² + B²)
• θ = 180° → R = |A − B|

4. Resolution of Vectors

Process of splitting a vector into perpendicular components.

R_x = R cosθ
R_y = R sinθ

R = √(R_x² + R_y²)
tanθ = R_y / R_x

5. Projectile Motion

Motion of a body projected into air and moving under gravity alone.

Velocity Components

u_x = u cosθ
u_y = u sinθ

Important Formulae

• Time of flight: T = (2u sinθ) / g
• Maximum height: H = (u² sin²θ) / (2g)
• Range: R = (u² sin2θ) / g

Key Points

• Horizontal velocity remains constant
• Vertical velocity changes due to gravity
• Maximum range at 45°

6. Relative Velocity

Velocity of one body with respect to another.

v_AB = v_A − v_B

Same & Opposite Direction

• Same direction → difference of speeds
• Opposite direction → sum of speeds

Applications

• Boat in river
• Aeroplane in wind
• Relative motion of vehicles

7. Important CET Points

• Vector addition & resolution formulas
• Projectile motion numericals
• Relative velocity same/opposite direction
• Use g = 10 m/s² unless stated otherwise