Projectile Motion Class 11 Physics (2026–27): Formula, Graphs & Solved Numericals

Introduction

Projectile Motion Class 11 Physics is one of the most important topics in mechanics that explains the motion of objects projected into the air under the influence of gravity. This chapter covers trajectory, time of flight, maximum height, horizontal range, derivations, graphs, and solved numericals for CBSE, JEE, and NEET preparation.

When a cricketer hits a six, a football travels through the air, or water comes out of a fountain, the object follows a curved path called projectile motion. Projectile motion is one of the most important topics in Class 11 Physics because it builds the foundation for mechanics and is frequently asked in CBSE, JEE, and NEET examinations.

In this chapter, we will learn projectile motion in the easiest possible way with formulas, derivations, real-life examples, graphs, solved numericals, and exam-oriented tips.

What is Projectile Motion?

Projectile motion is the motion of an object thrown into the air under the influence of gravity only.

After projection:

• Gravity acts vertically downward.
• No horizontal force acts on the object (ignoring air resistance).

Therefore:

• Horizontal motion is uniform.
• Vertical motion is accelerated due to gravity.

Real-Life Examples of Projectile Motion Class 11 Physics

Projectile motion can be seen everywhere in daily life:

• Cricket ball hit for a six
• Football kicked into the air
• Basketball throw
• Bullet fired from a gun
• Water fountain
• Cannon firing

All these objects move in a curved path called a parabolic path.

Characteristics/ Important Features of Projectile Motion

• Motion takes place in two dimensions.
• Horizontal velocity remains constant.
• Vertical velocity changes continuously.
• Trajectory of projectile is parabola.
• Acceleration due to gravity acts downward.

Types of Projectile Motion

Horizontal Projectile

Object is projected horizontally from a height.

Examples:

• Ball rolling off a table
• Bullet fired horizontally

Oblique Projectile

Object is projected at an angle with the horizontal.

Examples:

• Cricket shot
• Football kick
• Basketball throw

Components of Velocity

Suppose an object is projected with velocity u at angle θ.
Then the velocity has two components:

 

Horizontal Component

u_x = u cosθ

Vertical Component

u_y = u sinθ

Equations of Projectile Motion

Horizontal Motion

Since acceleration is zero in horizontal direction:

x = u cosθ × t

Vertical Motion

Using equation of motion:

y = u sinθ × t − ½gt²

Equation of Trajectory

Eliminating time from horizontal and vertical equations:

y = x tanθ − gx² / (2u² cos²θ)

This is the equation of a parabola.

Therefore, the path of projectile motion is parabolic.

Proof of Equation of Trajectory of a Projectile

Important Formulas of Projectile Motion

1. Time of Flight

T = 2u sinθ / g

2. Maximum Height

H = u² sin²θ / 2g

3. Horizontal Range

R = u² sin2θ / g

Proof of Formulae

Why is Range Maximum at 45°?

Range formula:

R = u² sin2θ / g

Maximum value of sin2θ is 1.

2θ = 90°

θ = 45°

Therefore, range is maximum at 45°.

To understand the basics of Motion in a Straight Line, students should also study our Motion in a Straight Line Class 11(2026-27): Key Strategy

Important Conceptual Points: Projectile Motion Class 11 Physics

1. Horizontal and Vertical Motions are Independent

• Gravity affects only vertical motion.
• Horizontal velocity remains constant.

2. Velocity at Highest Point

At highest point:

• Vertical velocity becomes zero.
• Horizontal velocity remains constant.

Therefore, projectile moves horizontally at the top point.

Solved Questions: Projectile Motion Class 11 Physics

Students preparing for Class 11 Physics should also practice concepts from Heat And Thermodynamics Physics Class 11 (2026-27)

Common Mistakes Students Make in Projectile Motion Class 11 Physics

1. Using sin instead of cos

Students often confuse horizontal and vertical components.

Correct:

• Horizontal → cos
• Vertical → sin

2. Forgetting Gravity Direction

Gravity always acts downward.

3. Wrong Angle in Range Formula

Remember:

• Range uses
  $\sin2\theta$ 

  $\sin 2\theta$

4. Mixing Units

Always use SI units.

For a better understanding of Dimensional Formula concepts, read our World of Dimensional Formula Class11: Expert Tips(2026-27)

Important Graphs in Projectile Motion Class 11 Physics

Students should practice:

• Trajectory graph
• Velocity-time graph
• Height-time graph
• Range-angle graph

These are frequently asked in board and competitive exams.

Memory Tricks: Projectile Motion Class 11 Physics

Easy Trick 1

Horizontal Motion = Uniform Motion

Vertical Motion = Free Fall Motion

Easy Trick 2

At highest point:

• Vertical velocity = 0

Exam Important Points: Projectile Motion Class 11 Physics

CBSE Board Exams

Most important topics:

• Time of flight
• Maximum height
• Horizontal range
• Derivations
• Numericals

JEE & NEET

Focus on:

• Conceptual questions
• Relative projectile motion
• Graph-based questions
• Formula applications

Students preparing for CBSE board exams should also check updates from CBSE Official Website

Quick Revision Table: Projectile Motion Class 11 Physics