Mastering Motion in a Plane: Vectors, Projectile Motion & JEE Strategy

Scalars and vectors are two different quantities with different SI Units. Scalar only tells us distance. Vectors indicate both distance and direction. 

You should be clear with the concepts of distance and direction, much like how speed and velocity are different from each other.    

There are some challenges you will face in the beginning while doing this section. 

• First, you will have to go out of the book and visualise vectors 
• Second, get ready for some trigonometry to explain components

When you multiply a vector by a scalar, you are lengthening the vector. The direction will change if the scalar is positive or negative.
For JEE like exams, this is directly used for solving problems using Newton’s second law. This is because this also is a scalar multiplication.

The 2nd law formula is F = ma, where F is force, m is mass, and a is acceleration. Mass is a scalar quantity as it does not have any direction. But force and acceleration are both vector quantities. Both force and acceleration are vector quantities. While mass is a scalar quantity with no direction, and only magnitude.

Vector Additions

For exams, remember the Parallelogram Law. For operations in vectors like addition and subtraction, this is needed.
It is used for combining forces, adding velocities when objects have relative motion and similar. 

Also, we have two more comprehensive guides on this section, aligning with your NCERT textbook. Do check.

• Addition and Subtraction of Vectors
• Vector Addition by Analytical Method

Most Important Things About Vector Operations 

• Confusion with Angles: In cosine law (R² = A² + B² + 2AB cos θ), θ is the angle between vectors when tails are joined
• Sign Errors: Be extra careful with negative components
• Magnitude vs Component: |A| is always positive. But, Ax can be negative

Vector components are basically looking into vectors as two different personalities. 

You can practically think of any vector as having an “x-personality” and a “y-personality”.  

These components will always act independently. 

In the real world, when you walk diagonally across a field, you're simultaneously moving east and north. Each component is independent.

Understanding Vector Components for Exams

While you can learn in-depth about vector resolution, here are some of the main approaches you should consider for your exams. 

• Standard Form: Always write vectors as Ax î + Ay ĵ
• Angle Relationships: Master the trigonometry. You have cos for adjacent, sin for opposite.
• Quadrant Awareness: Know your signs for each quadrant

How to Effectively Practice the Component Method

• Step 1: Draw the vector
• Step 2: Identify the angle with x-axis
• Step 3: Calculate Ax = A cos θ and Ay = A sin θ
• Step 4: Add components separately
• Step 5: Find resultant using Pythagorean theorem

If calculus scares you, remember, derivatives just mean the “rate of change.”

These are concepts you can remember as, 

• Velocity = how fast position changes. We show that as v = dr/dt
• Acceleration = how fast velocity changes. The acceleration formula is a = dv/dt

You can also go in-depth to learn differentiation and integration in Class 12 Maths. 

Every projectile follows a parabolic path because there are both horizontal and vertical motions. 

• During horizontal motion, there is no acceleration, if you ignore air resistance
• For vertical motion of the projectile, there is constant acceleration due to gravity. 

Solving Projectile Motion for Annual and JEE Main Questions

• Step 1: Identify the coordinate system (usually origin at launch point) 
• Step 2: Resolve initial velocity into components 
• Step 3: Apply kinematic equations separately for x and y directions 
• Step 4: Use boundary conditions (like y = 0 for range calculations)

Circular motion is described more in your next Physics chapter, where you see how the Newtonian Laws govern it. 

But in this chapter, you have to be conceptually clear about Uniform Circular Motion while answering the question

“How can something moving at constant speed be accelerating?”

One way to see it as acceleration is to change velocity. It’s not just changing speed. 

In circular motion, direction changes constantly, so acceleration is present. Then comes the concept, Centripetal Acceleration. 

The trick to understanding centripetal acceleration is to visualise it. 

Think of swinging a ball on a string. The ball “wants” to move in a straight line, where Newton’s First Law applies. But the string constantly “pulls” it toward the centre.

Key Formulas in Uniform Circular Motion

• ac = v²/r (using linear speed)
• ac = ω²r (using angular speed)
• v = rω (connecting linear and angular)

Strategy to Approach Questions on Uniform Circular Motion

• Always identify the centre of circular motion
• Draw the radius clearly
• Remember: acceleration points toward centre

Look for similar Physics notes for Class 11 below. 

Units and Measurements Class 11 Notes	Mechanical Properties of Solids Class 11 Notes
Motion in a Straight Line Class 11 Notes	Mechanical Properties of Fluids Class 11 Notes
NCERT Class 11 Notes for Motion in a Plane	Thermal Properties of Matter Class 11 Notes
Laws of Motion Class 11 Notes	Thermodynamics Class 11 Notes
Work, Energy, and Power Class 11 Notes	Kinetic Theory of Gas Class 11 Notes
System of Particles and Rotational Motion Class 11 Notes	Oscillations Class 11 Notes
Gravitation Class 11 Notes	Waves Class 11 Notes

Get an overview of other Science stream subjects below. 

NCERT Class 11 Notes for PCM

NCERT Class 11 Physics Notes