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.

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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.

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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

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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.

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