Projectile Motion Class 11 Physics Notes for NEET Beginners

  Easy Projectile Motion Notes with Formulas for NEET Students

PROJECTILE MOTION

│

├── Definition

│   ├── Object thrown in air

│   ├── Moves under gravity only

│   └── Called projectile

│

├── Examples

│   ├── Cricket ball

│   ├── Football

│   ├── Stone

│   └── Bullet

│

├── Types of Motion

│   │

│   ├── Horizontal Motion

│   │   ├── Along x-axis

│   │   ├── No acceleration

│   │   ├── Constant velocity

│   │   └── Uniform motion

│   │

│   └── Vertical Motion

│       ├── Along y-axis

│       ├── Gravity acts downward

│       ├── Acceleration = g

│       └── Non-uniform motion

│

├── Galileo’s Concept

│   ├── Horizontal and vertical motions independent

│   └── Explained in 1632

│

├── Assumptions

│   ├── Air resistance neglected

│   └── Only gravity acts

│

├── Initial Velocity

│   ├── Total velocity = v₀

│   ├── Angle of projection = θ

│   │

│   ├── Horizontal Component

│   │   └── v₀x = v₀ cosθ

│   │

│   └── Vertical Component

│       └── v₀y = v₀ sinθ

│

├── Acceleration

│   ├── ax = 0

│   └── ay = -g

│

├── Position Equations

│   │

│   ├── Horizontal Position

│   │   └── x = (v₀ cosθ)t

│   │

│   └── Vertical Position

│       └── y = (v₀ sinθ)t - ½gt²

│

├── Velocity Equations

│   │

│   ├── Horizontal Velocity

│   │   └── vx = v₀ cosθ

│   │

│   └── Vertical Velocity

│       └── vy = v₀ sinθ - gt

│

├── Maximum Height

│   ├── Highest point

│   ├── vy = 0

│   └── Projectile changes direction

│

├── Trajectory

│   ├── Path followed by projectile

│   └── Shape = Parabola

│

├── Important NEET Points

│   ├── Horizontal velocity constant

│   ├── Gravity acts downward only

│   ├── vy = 0 at top point

│   ├── Path is parabolic

│   └── Motions are independent

│

└── Quick Tricks

    ├── cosθ → Horizontal

    ├── sinθ → Vertical

    ├── x-motion → Uniform

    ├── y-motion → Accelerated

    └── Gravity acts vertically downward

Projectile motion showing horizontal and vertical components of motion with parabolic trajectory.

Dr.Sanjaykumar pawar

Internal Links

Laws of Motion Notes for NEET

Motion in a Straight Line Notes

Motion in a Plane Complete Guide

Kinematics Formula Sheet

Gravitation Notes for NEET

Vectors Physics Notes

Work, Energy and Power Notes

Circular Motion NEET Notes

Physics Formula Revision Notes

NEET Physics Chapterwise Notes

Projectile Motion Notes for NEET Beginners

1. What is Projectile Motion?

A body thrown into the air and moving under the effect of gravity only is called a projectile.

The motion of such a body is called projectile motion.

Examples:

• Cricket ball
• Football
• Stone thrown in air
• Bullet fired at an angle

2. Main Idea of Projectile Motion

Projectile motion consists of two independent motions happening together.

(a) Horizontal Motion

• Motion along x-axis
• No acceleration acts horizontally
• Velocity remains constant

(b) Vertical Motion

• Motion along y-axis
• Gravity acts downward
• Acceleration is constant

3. Galileo’s Contribution

Galileo first explained that horizontal and vertical motions are independent of each other.

4. Assumption in Projectile Motion

• Air resistance is neglected.
• Only gravity acts on the projectile.

5. Initial Velocity of Projectile

Suppose a projectile is thrown with:

• Initial velocity = v₀
• Angle of projection = θ

6. Components of Initial Velocity

(a) Horizontal Component

v_0x = v₀ cos θ

• Acts along x-axis
• Remains constant throughout motion

(b) Vertical Component

v_0y = v₀ sin θ

• Acts along y-axis
• Changes due to gravity

7. Acceleration of Projectile

a_x = 0

a_y = -g

• No horizontal acceleration
• Gravity acts vertically downward

8. Initial Position

x₀ = 0

y₀ = 0

This means the projectile starts from the origin.

9. Position of Projectile at Time t

(a) Horizontal Position

x = (v₀ cos θ)t

• Horizontal distance increases uniformly
• Depends on time and initial velocity

(b) Vertical Position

y = (v₀ sin θ)t - ½gt²

• Gravity slows upward motion
• Gravity increases downward motion

10. Velocity Components at Any Time

(a) Horizontal Velocity

v_x = v₀ cos θ

Horizontal velocity remains constant.

(b) Vertical Velocity

v_y = v₀ sin θ - gt

Vertical velocity changes continuously because of gravity.

11. Maximum Height

At the highest point:

v_y = 0

• Projectile stops moving upward for a moment
• Then it starts moving downward

12. Shape of Projectile Path

The path followed by a projectile is called a trajectory.

The trajectory of projectile motion is always a parabola.

13. Important NEET Points

• Horizontal velocity remains constant.
• Gravity acts only downward.
• Vertical velocity becomes zero at maximum height.
• Projectile path is parabolic.
• Horizontal and vertical motions are independent.

14. Formula Summary

Horizontal Velocity:

v_x = v₀ cos θ

Vertical Velocity:

v_y = v₀ sin θ - gt

Horizontal Position:

x = (v₀ cos θ)t

Vertical Position:

y = (v₀ sin θ)t - ½gt²

15. Quick Revision Tricks

• cos θ → Horizontal component
• sin θ → Vertical component
• Horizontal motion → Constant velocity
• Vertical motion → Accelerated motion
• At highest point → v_y = 0

16. Conclusion

Projectile motion is a combination of:

• Uniform horizontal motion
• Vertically accelerated motion under gravity

Prepared for NEET Physics Beginners

Projectile Motion Question Bank

Class 11 CBSE Physics

1. Multiple Choice Questions (MCQs)

Q1. A projectile moves in a parabolic path because:

a) Horizontal velocity changes
b) Vertical velocity remains constant
c) Horizontal and vertical motions are independent
d) Gravity acts horizontally

Answer: c) Horizontal and vertical motions are independent

Q2. The acceleration of a projectile at highest point is:

a) Zero
b) g upward
c) g downward
d) Infinite

Answer: c) g downward

Q3. At maximum height, vertical velocity becomes:

a) Maximum
b) Minimum
c) Zero
d) Infinite

Answer: c) Zero

Q4. The horizontal component of velocity:

a) Increases
b) Decreases
c) Remains constant
d) Becomes zero

Answer: c) Remains constant

2. Very Short Answer Questions

Q1. What is a projectile?

A body thrown into air moving under gravity only is called a projectile.

Q2. What is the shape of projectile path?

Parabola.

Q3. What is horizontal acceleration in projectile motion?

Zero.

Q4. What happens to vertical velocity at highest point?

It becomes zero.

3. Short Answer Questions

Q1. Why is projectile motion called two-dimensional motion?

Projectile motion has both horizontal and vertical components of motion. Therefore it is called two-dimensional motion.

Q2. Why does horizontal velocity remain constant?

No horizontal force acts on the projectile. Therefore horizontal acceleration is zero and horizontal velocity remains constant.

Q3. State two assumptions in projectile motion.

1. Air resistance is neglected.
2. Only gravity acts on the projectile.

Q4. Write equations of horizontal and vertical positions.

x = (v₀ cosθ)t

y = (v₀ sinθ)t − ½gt²

4. Long Answer Questions

Q1. Explain projectile motion with equations.

Projectile motion is the motion of an object thrown into air under the influence of gravity only. It has two independent motions:

• Horizontal Motion: No acceleration acts horizontally. Therefore horizontal velocity remains constant.
• Vertical Motion: Gravity acts vertically downward. Therefore vertical velocity changes continuously.

Initial velocity components:

v₀x = v₀ cosθ
v₀y = v₀ sinθ

Position equations:

x = (v₀ cosθ)t
y = (v₀ sinθ)t − ½gt²

Velocity equations:

vx = v₀ cosθ
vy = v₀ sinθ − gt

The path followed by projectile is a parabola.

5. Assertion and Reason Questions

Q1. Assertion (A): At maximum height, vertical velocity becomes zero.

Reason (R): Gravity stops acting at maximum height.

Assertion is true but Reason is false.

Q2. Assertion (A): Horizontal velocity remains constant.

Reason (R): No horizontal acceleration acts on projectile.

Both Assertion and Reason are true and Reason correctly explains Assertion.

6. Fill in the Blanks

1. The path of projectile is __________.

Parabola

2. Horizontal acceleration in projectile motion is __________.

Zero

3. At highest point vertical velocity becomes __________.

Zero

4. Gravity acts in __________ direction.

Downward

7. Case Study Questions

A boy throws a ball with velocity v₀ at angle θ. The ball moves along a curved path and returns to ground.

Q1. What type of motion is this?

Projectile motion.

Q2. What is the shape of path?

Parabola.

Q3. Which force acts on the ball?

Gravitational force.

Q4. What happens to horizontal velocity?

It remains constant.

8. Statement Based Questions

1. Gravity acts horizontally in projectile motion.

False

2. Horizontal velocity remains constant.

True

3. Projectile motion is one-dimensional.

False

4. Vertical acceleration equals g.

True

9. Match the Columns

Column A	Column B
1. Horizontal acceleration	a. Parabola
2. Path of projectile	b. Zero
3. Vertical acceleration	c. g
4. Highest point	d. vy = 0

Answers:

1 → b
2 → a
3 → c
4 → d

10. HOTS Questions

Q1. Why does a projectile eventually fall to ground?

Gravity continuously pulls the projectile downward causing it to return to ground.

Q2. Can horizontal velocity become zero during projectile motion?

No. No horizontal acceleration acts on projectile.

11. Important Formulae

v₀x = v₀ cosθ

v₀y = v₀ sinθ

x = (v₀ cosθ)t

y = (v₀ sinθ)t − ½gt²

vx = v₀ cosθ

vy = v₀ sinθ − gt

Prepared for CBSE Class 11 Physics Students

Acceleration Notes for Class 11 Physics CBSE & NEET

 Acceleration

│

├── Definition

│   ├── Rate of change of velocity

│   ├── Vector quantity

│   └── Has magnitude + direction

│

├── Velocity Change

│   ├── Change in speed

│   ├── Change in direction

│   └── Both speed and direction

│

├── Average Acceleration

│   ├── Formula

│   │   └── a = Δv / Δt

│   │

│   ├── Terms

│   │   ├── Δv = change in velocity

│   │   └── Δt = time interval

│   │

│   └── Direction

│       └── Same as Δv

│

├── Instantaneous Acceleration

│   ├── Acceleration at a particular instant

│   ├── Very small time interval

│   └── Formula

│       └── a = dv / dt

│

├── Motion in x-y Plane

│   ├── Velocity Components

│   │   ├── vx = v cosθ

│   │   └── vy = v sinθ

│   │

│   ├── Acceleration Components

│   │   ├── ax = dvx/dt

│   │   └── ay = dvy/dt

│   │

│   └── Vector Form

│       └── a = ax i + ay j

│

├── Graphical Understanding

│   ├── Velocity changes from point to point

│   ├── Δv found by vector subtraction

│   ├── Smaller Δt gives accurate acceleration

│   └── Δt → 0 gives instantaneous acceleration

│

├── Units

│   ├── SI Unit

│   │   └── m/s²

│   │

│   └── Dimensional Formula

│       └── [M⁰L¹T⁻²]

│

├── Special Cases

│   ├── Constant velocity

│   │   └── Acceleration = 0

│   │

│   ├── Negative acceleration

│   │   └── Retardation / Deceleration

│   │

│   └── Circular motion

│       └── Acceleration exists due to direction change

│

└── Important NEET Formulas

    ├── a = Δv / Δt

    ├── a = dv / dt

    ├── ax = dvx / dt

    ├── ay = dvy / dt

    ├── vx = v cosθ

    └── vy = v sinθ 

Class 11 Physics Acceleration Notes with
 Formulas and Vector Components for CBSE and NEET Students 

- Dr.Sanjaykumar pawar

 

Acceleration Notes (NEET Level)

1. What is Acceleration?

Acceleration tells us how quickly velocity changes with time.

• If speed changes → acceleration exists.
• If direction changes → acceleration exists.
• If both change → acceleration exists.

Acceleration is a vector quantity because it has both magnitude and direction.

---

2. Average Acceleration

Average acceleration is defined as:

Average Acceleration = Change in Velocity / Time Interval

a = Δv / Δt

Where:

• a = average acceleration
• Δv = change in velocity
• Δt = time interval

---

3. Velocity Components in x-y Plane

In two-dimensional motion, velocity has two components:

• vx → velocity along x-axis
• vy → velocity along y-axis

Δv = Δvx i + Δvy j

Therefore acceleration becomes:

a = (Δvx / Δt)i + (Δvy / Δt)j

Where:

• i = unit vector along x-axis
• j = unit vector along y-axis

---

4. Components of Acceleration

a = ax i + ay j

Where:

• ax = acceleration along x-axis
• ay = acceleration along y-axis

---

5. Instantaneous Acceleration

Instantaneous acceleration means acceleration at a particular instant of time.

It is obtained when the time interval becomes extremely small.

a = lim (Δt → 0) (Δv / Δt)

---

6. Component Form of Instantaneous Acceleration

ax = dvx / dt

ay = dvy / dt

Meaning:

• ax = rate of change of velocity along x-axis
• ay = rate of change of velocity along y-axis

---

7. Graphical Understanding of Acceleration

Suppose an object moves from point P to another point after a small time interval Δt.

• The velocity changes from v to another value.
• The change in velocity is called Δv.
• The direction of acceleration is same as the direction of Δv.

As Δt becomes smaller:

• Average acceleration approaches instantaneous acceleration.
• The direction becomes more accurate.

---

8. Velocity Components

If velocity makes angle θ with x-axis:

vx = v cos θ

vy = v sin θ

Where:

• vx = horizontal component
• vy = vertical component

---

9. SI Unit of Acceleration

m/s²

Read as: metre per second square

---

10. Dimensional Formula

[M⁰L¹T⁻²]

---

11. Important NEET Points

• Acceleration depends on change in velocity.
• Constant velocity means acceleration is zero.
• Negative acceleration is called retardation or deceleration.
• In circular motion, acceleration exists even if speed is constant because direction changes continuously.

---

12. Formula Summary Table

Concept	Formula
Average Acceleration	a = Δv / Δt
Instantaneous Acceleration	a = dv / dt
x-component	ax = dvx / dt
y-component	ay = dvy / dt
Velocity Components	vx = v cos θ, vy = v sin θ

Quick Revision

• Acceleration = Rate of change of velocity.
• It is a vector quantity.
• SI unit = m/s².
• Velocity change can be due to speed or direction change.
• Average acceleration uses finite time interval.
• Instantaneous acceleration uses very small time interval.

Class 11 Physics - Acceleration Questions and Answers

1. Multiple Choice Questions (MCQs)

Q1. Acceleration is defined as:

A. Change in displacement
B. Change in speed
C. Change in velocity per unit time
D. Distance travelled per unit time

Answer: C. Change in velocity per unit time

Q2. SI unit of acceleration is:

A. m/s
B. m/s²
C. m²/s
D. km/h

Answer: B. m/s²

Q3. Which of the following is a vector quantity?

A. Distance
B. Speed
C. Time
D. Acceleration

Answer: D. Acceleration

2. Very Short Answer Questions

Q1. Define acceleration.

Answer: Acceleration is the rate of change of velocity with time.

Q2. Write the SI unit of acceleration.

Answer: m/s²

Q3. Is acceleration a scalar or vector quantity?

Answer: Vector quantity.

3. Short Answer Questions

Q1. Differentiate between average acceleration and instantaneous acceleration.

Average Acceleration	Instantaneous Acceleration
Calculated over a finite time interval	Calculated at a particular instant
a = Δv / Δt	a = dv / dt
Gives average change	Gives exact change

Q2. Why is acceleration a vector quantity?

Answer: Acceleration depends on change in velocity. Since velocity has both magnitude and direction, acceleration is also a vector quantity.

4. Long Answer Questions

Q1. Define average acceleration and derive its formula.

Average acceleration is the change in velocity divided by time interval.

If initial velocity = u
Final velocity = v
Time taken = Δt

Change in velocity:

Δv = v - u

Therefore,

a = Δv / Δt

Answer: Average acceleration is equal to change in velocity divided by time interval.

Q2. Explain instantaneous acceleration.

Instantaneous acceleration is acceleration at a particular instant of time. It is obtained when the time interval becomes extremely small.

a = dv / dt

Answer: Instantaneous acceleration gives exact acceleration at any instant.

5. Assertion and Reason Questions

Q1.

Assertion (A): Acceleration is a vector quantity.
Reason (R): Acceleration depends on change in velocity.

A. Both A and R are true and R is correct explanation of A
B. Both A and R are true but R is not correct explanation
C. A is true but R is false
D. A is false but R is true

Answer: A

6. Fill in the Blanks

1. Acceleration is the rate of change of _______.

Answer: velocity

2. SI unit of acceleration is _______.

Answer: m/s²

3. Negative acceleration is called _______.

Answer: retardation

7. Case Study Questions

A car moves along a straight road. Its velocity changes from 10 m/s to 30 m/s in 5 seconds.

Q1. What is the change in velocity?

Answer: 20 m/s

Q2. Calculate acceleration.

a = (v - u)/t

a = (30 - 10)/5 = 4 m/s²

Answer: 4 m/s²

8. Statement Based Questions

Q1. Acceleration can exist without change in speed.

Answer: True

Q2. A body moving in circular path has acceleration.

Answer: True

Q3. Velocity and acceleration always act in same direction.

Answer: False

9. Match the Columns

Column A	Column B
1. Acceleration	a. m/s²
2. Velocity	b. Vector quantity
3. Retardation	c. Negative acceleration
4. SI unit of acceleration	d. Rate of change of displacement

Answers:
1 → b
2 → d
3 → c
4 → a

10. Important Formula Questions

Q1. Write formula for average acceleration.

a = Δv / Δt

Q2. Write formula for instantaneous acceleration.

a = dv / dt

Q3. Write acceleration components in x and y directions.

ax = dvx/dt
ay = dvy/dt

Internal Links

Motion in a Straight Line Notes

Motion in a Plane Notes

Velocity and Speed Difference

Vector Quantities in Physics

Newton’s Laws of Motion

Kinematics Formula Sheet

NEET Physics Important Questions

CBSE Class 11 Physics Chapter Wise Notes

Projectile Motion Notes

Units and Dimensions Notes

Resolution of Vectors Class 11 Physics Notes, MCQs & Examples (NEET + CBSE)

 RESOLUTION OF VECTORS

│

├── 1. Meaning

│   ├── Splitting a vector into components

│   ├── Components add to form original vector

│   └── Used in force, motion, displacement problems

│

├── 2. Vector Resolution in Plane

│   ├── Vector A resolved along vectors a and b

│   ├── Formula:

│   │      A = λa + μb

│   ├── λ and μ are real numbers

│   └── Component vectors:

│          ├── λa

│          └── μb

│

├── 3. Unit Vectors

│   ├── Magnitude = 1

│   ├── Show direction only

│   ├── No dimension or unit

│   ├── Along axes:

│   │      ├── î → x-axis

│   │      ├── ĵ → y-axis

│   │      └── k̂ → z-axis

│   └── Properties:

│          ├── |î| = |ĵ| = |k̂| = 1

│          └── Mutually perpendicular

│

├── 4. Vector in Unit Vector Form

│   ├── Formula:

│   │      A = |A| n̂

│   ├── |A| → magnitude

│   └── n̂ → unit vector along A

│

├── 5. Resolution Along x and y Axes

│   ├── Vector A in x-y plane

│   ├── Components:

│   │      ├── Ax along x-axis

│   │      └── Ay along y-axis

│   └── Vector form:

│          A = Ax î + Ay ĵ

│

├── 6. Component Formulae

│   ├── Ax = A cosθ

│   ├── Ay = A sinθ

│   └── θ = angle with x-axis

│

├── 7. Nature of Components

│   ├── Positive

│   ├── Negative

│   └── Zero

│

├── 8. Magnitude of Vector

│   └── Formula:

│          A = √(Ax² + Ay²)

│

├── 9. Direction of Vector

│   ├── tanθ = Ay/Ax

│   └── θ = tan⁻¹(Ay/Ax)

│

├── 10. Ways to Represent Vector

│   ├── By magnitude and direction

│   │      ├── A

│   │      └── θ

│   └── By components

│          ├── Ax

│          └── Ay

│

├── 11. Resolution in 3D

│   ├── Components:

│   │      ├── Ax = A cosα

│   │      ├── Ay = A cosβ

│   │      └── Az = A cosγ

│   ├── Vector form:

│   │      A = Ax î + Ay ĵ + Az k̂

│   └── Magnitude:

│          A = √(Ax² + Ay² + Az²)

│

├── 12. Position Vector

│   └── r = xî + yĵ + zk̂

│

├── 13. NEET Important Points

│   ├── x-component → cosine

│   ├── y-component → sine

│   ├── Components are scalars

│   └── Axî and Ayĵ are vectors

│

└── 14. Common Mistakes

    ├── Wrong sign of components

    ├── Confusing sin and cos

    ├── Ignoring quadrant

    └── Treating Ax as vector

Resolution of a vector into x and y components showing Ax = A cosθ and Ay = A sinθ on Cartesian axes.

 

- Dr.Sanjaykumar pawar

Internal Links 

/class-11-physics-vectors

/motion-in-a-plane-notes

/neet-physics-important-formulas

/physics-mcqs-class-11

/unit-vectors-and-components

/cbse-class-11-physics-notes

/physics-numericals-practice-set

Resolution of Vectors – NEET Notes

1. Meaning of Resolution of Vectors

Resolution of a vector means splitting a vector into two or more parts called components.

These components combine together to form the original vector.

Example: A diagonal force can be divided into horizontal and vertical components.

---

2. Resolving a Vector in a Plane

Let there be two vectors a and b in the same plane. Another vector A can be written as:

A = λa + μb

Where:

• λ and μ are real numbers
• λa and μb are component vectors

Vector A is said to be resolved into components along vectors a and b.

---

3. Unit Vectors

A unit vector is a vector having magnitude equal to 1.

It is used only to represent direction.

Unit Vectors Along Coordinate Axes

• Along x-axis → î
• Along y-axis → ĵ
• Along z-axis → k̂

|î| = |ĵ| = |k̂| = 1

Unit vectors have no dimensions and no units.

---

4. Vector in Terms of Unit Vector

Any vector can be written as:

A = |A| n̂

Where:

• |A| = magnitude of vector
• n̂ = unit vector in direction of A

---

5. Resolution Along x and y Axes

A vector A in a plane can be resolved into x-component and y-component.

A = Ax î + Ay ĵ

Where:

• Ax = x-component
• Ay = y-component

---

6. Formula for Components

If vector A makes angle θ with x-axis:

Ax = A cosθ

Ay = A sinθ

x-component uses cosine and y-component uses sine.

---

7. Sign of Components

Components can be positive, negative, or zero depending on direction.

Quadrant	x-component	y-component
First	Positive	Positive
Second	Negative	Positive
Third	Negative	Negative
Fourth	Positive	Negative

---

8. Magnitude of Vector

If Ax and Ay are known:

A = √(Ax² + Ay²)

This formula is based on Pythagoras theorem.

---

9. Direction of Vector

tanθ = Ay / Ax

Therefore:

θ = tan⁻¹(Ay / Ax)

---

10. Two Ways to Represent a Vector

Method 1

• Magnitude A
• Direction θ

Method 2

• x-component Ax
• y-component Ay

---

11. Resolution in Three Dimensions

In 3D, a vector has three components:

Ax = A cosα

Ay = A cosβ

Az = A cosγ

Where:

• α = angle with x-axis
• β = angle with y-axis
• γ = angle with z-axis

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12. Vector Form in 3D

A = Ax î + Ay ĵ + Az k̂

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13. Magnitude in 3D

A = √(Ax² + Ay² + Az²)

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14. Position Vector

A position vector is written as:

r = x î + y ĵ + z k̂

Where x, y, z are coordinates of the point.

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15. NEET Important Points

• Resolution means splitting vectors into components.
• Unit vectors show direction only.
• î, ĵ, k̂ are unit vectors.
• Ax = A cosθ
• Ay = A sinθ
• A = √(Ax² + Ay²)
• tanθ = Ay / Ax

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16. Common NEET Mistakes

• Forgetting signs of components
• Confusing sine and cosine
• Ignoring quadrant rules
• Writing scalar as vector

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17. Quick Trick for NEET

• Cos → adjacent side
• Sin → opposite side
• x-component → cosine
• y-component → sine

Prepared for NEET Physics Students

Class 11 Physics - Resolution of Vectors

1. Multiple Choice Questions (MCQs)

Q1. Resolution of a vector means:

(a) Adding vectors
(b) Splitting into components
(c) Multiplying vectors
(d) Rotating vectors

Answer: (b) Splitting into components

Q2. Unit vector has magnitude:

(a) 0 (b) 1 (c) 2 (d) infinite

Answer: (b) 1

Q3. x-component of vector A is:

(a) A sinθ (b) A cosθ (c) A tanθ (d) A cotθ

Answer: (b) A cosθ

Q4. Unit vector along x-axis is:

Answer: î

2. Very Short Answer Questions

Q1. Define resolution of vectors.

Answer: Splitting a vector into components along different directions.

Q2. What is unit vector?

Answer: A vector with magnitude 1 that shows direction only.

Q3. Name unit vectors.

Answer: î, ĵ, k̂

3. Short Answer Questions

Q1. Write vector in component form.

Answer: A = Ax î + Ay ĵ

Q2. Why are components useful?

Answer: They simplify calculations in physics problems.

4. Long Answer Questions

Q1. Explain resolution of vector in 2D.

A vector A making angle θ with x-axis can be resolved into components:
Ax = A cosθ
Ay = A sinθ
A = Ax î + Ay ĵ
Magnitude: A = √(Ax² + Ay²)

5. Assertion and Reason

Q1.

Assertion: Unit vectors have magnitude 1.
Reason: They are used to represent direction only.

Answer: Both are true and Reason is correct explanation.

6. Fill in the Blanks

Q1. Resolution means splitting vector into ______.

Answer: components

Q2. Unit vector along y-axis is ______.

Answer: ĵ

7. Match the Column

î → x-axis
ĵ → y-axis
k̂ → z-axis
Ax → x-component

8. Case Study

A force of 20 N makes 30° with x-axis.

Q1. Find Ax

Answer: Ax = 20 cos30 = 10√3 N

Q2. Find Ay

Answer: Ay = 20 sin30 = 10 N

9. Numericals

Q1. Find magnitude of vector (3,4)

Answer: √(3² + 4²) = 5