What is motion in a plane?

Motion in a plane is motion of a particle in two dimensions, where its position, velocity, and acceleration are represented by vectors in an \(x\text{-}y\) plane.

What is a scalar quantity?

A scalar quantity is one that has only magnitude and no direction, such as mass, distance, speed, time, or temperature.

What is a vector quantity?

A vector quantity has both magnitude and direction, such as displacement, velocity, acceleration, and force.

Define position vector in a plane.

Position vector \(\vec{r}\) of a particle at \((x,y)\) is given by \(\vec{r}=x\hat{i}+y\hat{j}\) with respect to the origin \(O(0,0)\).

Define displacement vector.

Displacement vector is the change in position: \(\Delta\vec{r}=\vec{r}_2-\vec{r}_1\), independent of the actual path followed.

Write the expressions for average velocity in a plane.

Average velocity is \(\vec{v}_{\text{avg}}=\frac{\Delta\vec{r}}{\Delta t}\), where \(\Delta\vec{r}\) is displacement in time interval \(\Delta t\).

What is instantaneous velocity in 2D?

Instantaneous velocity is \(\vec{v}=\frac{d\vec{r}}{dt}\) and is always tangent to the path at that instant.

Define average acceleration in a plane.

Average acceleration is \(\vec{a}_{\text{avg}}=\frac{\Delta\vec{v}}{\Delta t}\), where \(\Delta\vec{v}\) is change in velocity in time \(\Delta t\).

What is instantaneous acceleration in a plane?

Instantaneous acceleration is \(\vec{a}=\frac{d\vec{v}}{dt}\) and measures the rate of change of velocity vector at a given instant.

State the triangle law of vector addition.

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

State the parallelogram law of vector addition.

If two vectors from the same point form adjacent sides of a parallelogram, the diagonal through that point gives the resultant vector.

Give formula for magnitude of resultant of two vectors.

For vectors \(\vec{A}\) and \(\vec{B}\) with angle \(\theta\) between them, resultant magnitude is \(R=\sqrt{A^2+B^2+2AB\cos\theta}\).

What is vector subtraction?

Vector subtraction \(\vec{A}-\vec{B}\) is defined as \(\vec{A}+(-\vec{B})\), where \(-\vec{B}\) has same magnitude as \(\vec{B}\) but opposite direction.

What is a unit vector?

A unit vector has magnitude 1 and gives only direction; unit vector along \(\vec{A}\) is \(\hat{A}=\frac{\vec{A}}{|\vec{A}|}\)

Give components of a vector in a plane.

If \(\vec{A}\) makes angle \(\theta\) with positive \(x\)-axis, then \(A_x=A\cos\theta\), \(A_y=A\sin\theta\), and \(\vec{A}=A_x\hat{i}+A_y\hat{j}\).

JEE · NEET · AIIMS · BITSAT · KVPY

✈️ Master Motion in a Plane
NCERT Class 11 · Chapter 3

Real PYQs from top competitive exams — filter by exam, attempt each question, track your progress and submit to see your full score report.

Attempt PYQs Study Strategy

Projectile MotionCircular MotionVectorsRelative Velocity 2DRange & Height

Real PYQs

Exam Bodies

15+

Years Covered

~9%

Exam Weightage

PYQs Overview

🎯

Projectile Motion

Range, max height, time of flight, angle of projection — #1 most asked.

★★★★★

96% Frequency

🔄

Uniform Circular Motion

Centripetal acceleration a=v²/r, angular velocity, frequency.

★★★★★

88% Frequency

📐

Vector Addition & Resolution

Parallelogram law, components, dot and cross products.

★★★★☆

82% Frequency

🌊

Relative Velocity in 2D

Rain-man problem, river-boat problem — angle and minimum time.

★★★★☆

74% Frequency

⬆️

Projectile on Inclined Plane

Range on incline, angle for maximum range on incline.

★★★★☆

68% Frequency

🔢

Angular Quantities

θ, ω, α relationships; angular and linear velocity connection.

★★★☆☆

60% Frequency

Topic Frequency

Projectile Motion (Range/Height) 96%

Uniform Circular Motion 88%

Vector Resolution 82%

2D Relative Velocity 74%

Inclined Plane Projectile 68%

Angular Kinematics 60%

Scalar & Vector Products 55%

💡 Did You Know?

Projectile in every single JEE paper since 2000
River-boat problem — asked 10× in NEET
Horizontal projectile — zero skips in BITSAT
Range = u²sin2θ/g: max at 45° — asked every year
Chapter 4 = highest marks density in Unit 1

Key Takeaways

🔑

Horizontal and vertical motions are independent

H: uniform velocity. V: free fall. Combine using SUVAT.

⚡

Range R = u²sin2θ/g; max at θ = 45°

Complementary angles (θ and 90°–θ) give the same range.

📐

Centripetal acceleration = v²/r = ω²r

Always directed toward the centre of the circle.

🌊

River-boat minimum drift: upstream angle

sin θ = v_river / v_boat gives angle to swim straight across.

🧮

Resultant of two vectors: √(A²+B²+2ABcosθ)

For perpendicular vectors: R = √(A²+B²).

🎯

Time of flight T = 2u sinθ/g

Depends only on vertical component; horizontal range = u cosθ × T.

Study Strategy

Vector AlgebraDay 1–2

Addition, subtraction, resolution, dot product, cross product.

Projectile BasicsDay 3

Derive all formulae from first principles. Know all 6 key formulae.

Projectile NumericalsDay 4

30+ problems: range, height, time, velocity at any point.

Circular MotionDay 5

Centripetal acceleration, period, frequency, angular velocity.

Relative Velocity 2DDay 6

Rain-man, river-boat — 15 problems of each type.

Attempt All PYQsDay 7

Projectile range and circular motion are highest-frequency topics.

Mock TestDay 8

30-Q timed; mix of projectile, circular, vector questions.

🗓️ 8-Day Chapter Plan

Day 1–2	Vector Algebra
Day 3	Projectile Basics
Day 4	Projectile Numericals
Day 5	Circular Motion
Day 6	Relative Velocity 2D
Day 7	Attempt All PYQs
Day 8	Mock Test

🧠 Pro Tip: Projectile problems become trivial once you internalize: horizontal = constant velocity, vertical = free fall. No exceptions.

🚀

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✈️ Master Motion in a Plane NCERT Class 11 · Chapter 3

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NCERT Class 11 · Chapter 3

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