Motion in a Plane – Lecture 3 | Class 11 Physics | Sumit Sharma Classes, Dhakoli Zirakpur

Welcome back to Sumit Sharma Classes! In this third lecture on Motion in a Plane, we will dive deeper into key concepts like projectile motion, relative velocity, and uniform circular motion. If you missed the previous lectures, make sure to check them out to build a strong foundation.

1. Projectile Motion

Projectile motion is a classic example of two-dimensional motion where an object moves under the influence of gravity alone.

Key Points:

  • Path of a Projectile: Parabolic trajectory.

  • Horizontal Motion: Uniform velocity (no acceleration).

  • Vertical Motion: Accelerated motion due to gravity (a = g = 9.8 m/s²).

Equations of Projectile Motion:

  • Time of Flight (T):

    T=2usin⁡θgT=g2usinθ​

  • Maximum Height (H):

    H=u2sin⁡2θ2gH=2gu2sin2θ​

  • Horizontal Range (R):

    R=u2sin⁡2θgR=gu2sin2θ​

    *(Maximum range at θ = 45°)*

Example:

A ball is thrown at 20 m/s at an angle of 30°. Find its time of flight, maximum height, and range.

2. Relative Velocity in Two Dimensions

Relative velocity helps us understand the motion of an object with respect to another moving object.

Formula:

V⃗AB=V⃗A−V⃗BVAB​=VA​−VB​

Where:

  • Vₐ = Velocity of object A

  • Vᵦ = Velocity of object B

  • Vₐᵦ = Velocity of A relative to B

Example:

If a boat moves at 10 km/h in still water and the river flows at 5 km/h, find the boat’s resultant velocity when moving:

  • Downstream (Same direction) → 15 km/h

  • Upstream (Opposite direction) → 5 km/h

3. Uniform Circular Motion

When an object moves in a circular path at constant speed, it undergoes uniform circular motion (UCM).

Key Concepts:

  • Centripetal Force (F_c): Keeps the object moving in a circle.

    Fc=mv2rFc​=rmv2​

  • Angular Velocity (ω):

    ω=vr=2πTω=rv​=T2π​

  • Time Period (T): Time for one complete revolution.

Example:

A car moves in a circular track of radius 50 m at 20 m/s. Find its centripetal acceleration.

Understanding motion in a plane is crucial for mastering physics. In this lecture, we covered:
✅ Projectile Motion (Equations & Applications)
✅ Relative Velocity (2D Motion)
✅ Uniform Circular Motion (Centripetal Force & Angular Velocity)

For detailed explanations, numerical problems, and live demonstrations, join us at Sumit Sharma Classes, Dhakoli Zirakpur.