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