# Projectile Motion Class 11 CBSE Physics Chapter 4 Motion in a Plane

Projectile motion is one of type of motion in a two-dimensional plane under an impact of gravitational force, it is the path of motion traversed by a thrown object towards the sky by an angle θ from the horizon. The path of the object is maintained by two components of the velocity, a vertical component towards the direction of the y-axis and a horizontal component towards the x-axis, both of these components are responsible to form a curved path of the object, such a motion is known as projectile motion.

**Projectile Motion Class 11 CBSE Physics Chapter 4 Motion in a Plane**

The path of the trajectory of the projectile is given as follows

Let the angle of projection is θ, and the object is thrown with the u velocity, since the motion is in two-dimensional plane Y and X axis, therefore considering the two component of velocity one is towards the y-axis and another towards the x-axis.

Let the components of motion towards the y-axis is u_{y} and towards the x-axis is u_{x}

u_{y} = usinθ (vertical component of velocity)and u_{x} = ucosθ(horizontal component of velocity)

In this motion, acceleration is due to the gravity is along the y-axis,in x -direction its value is 0,a_{x}=0

Since there is no acceleration in the x direction, therefore the velocity u_{x} = ucosθ will remain constant and in the direction of y(i.e for the vertical component) the acceleration is always -g,a_{y} = -g

The initial velocity of the obect in y direction is usinθ and when it obtained maximum height H(i.e point B),the vertical component of velocity,v_{y} becomes 0,v_{y} = 0

From A to B the velocity of the object decreases and from B to C ,the velocity of the object decreases

Note: The parameters are considered in this motion supposing air resistance is zero

Let the time taken by the flight of the object is =T

Maximum height (the distance of point B from the ground)=H

The range of the object(horizontal distance from A to C)=R

Let’s consider the motion from A to B.

The maximum height of the object is gained due to the y component of the velocity

The initial y component of the velocity is u_{y} = usinθ and the final velocity (i.e at B) =V_{y} =0

Applying the first equation of the motion

v = u +at

0 = usinθ -gt

gt = usinθ

t = usinθ/g

The time taken from A to B and B to C will be the same due to the conservational law of energy

**∴T = 2usinθ/g**

Now applying third equation of the motion for determining maximum height of the projectile

v² = u² +2as

The initial y component of the velocity is u_{y} = usinθ and the final velocity (i.e at B) =V_{y} =0

0= (usinθ)² +2(-g)H

2gH = u²sin²θ

**H = u²sin²θ/2g**

Since the range, AC is in the horizontal direction, therefore, considering the horizontal component of the velocity

Initial velocity in the x-direction,u_{x} = ucosθ and final velocity(i.e at C) = v_{x} =0 ,acceleration along x axis is 0

Applying second equation of the motion

s = ut + (1/2) at²

R = ucosθ.T + (1/2) ×0×T²

Substituting the value of T

R = ucosθ.2usinθ/g

R = u²2cosθsinθ/g

**R = u²sin 2θ/g**

**Circular Motion: Angular velocity and angular displacement**

**Addition of Vectors: CBSE Class 11 Physics Chapter 4 -Motion in a Plane**

Don’t forget to write a comment, subscribe us for the posts related to your study

**Electronic Configuration of s,p and d orbitals**

**Atomic Radius Class 11 Chemistry Chapter 3 Periodicity in Properties**

**Why does a Rainbow look like a Bow?**

**NCERT Solutions of Science and Maths for Class 9,10,11 and 12**

**NCERT Solutions for class 9 maths**

**NCERT Solutions for class 9 science **

**NCERT Solutions for class 10 maths**

**Class 10 Maths Question Paper CBSE Half Yearly Exam 2022 With Solutions**

**CBSE Class 10-Question paper of maths 2021 with solutions**

**CBSE Class 10-Half yearly question paper of maths 2020 with solutions**

**CBSE Class 10 -Question paper of maths 2020 with solutions**

**CBSE Class 10-Question paper of maths 2019 with solutions**

**NCERT Solutions for Class 10 Science**

**NCERT Solutions for class 11 maths**

Chapter 1-Sets | Chapter 9-Sequences and Series |

Chapter 2- Relations and functions | Chapter 10- Straight Lines |

Chapter 3- Trigonometry | Chapter 11-Conic Sections |

Chapter 4-Principle of mathematical induction | Chapter 12-Introduction to three Dimensional Geometry |

Chapter 5-Complex numbers | Chapter 13- Limits and Derivatives |

Chapter 6- Linear Inequalities | Chapter 14-Mathematical Reasoning |

Chapter 7- Permutations and Combinations | Chapter 15- Statistics |

Chapter 8- Binomial Theorem | Chapter 16- Probability |

**CBSE Class 11-Question paper of maths 2015**

**CBSE Class 11 – Second unit test of maths 2021 with solutions**

**NCERT Solutions for Class 11 Physics**

**chapter 3-Motion in a Straight Line**

**NCERT Solutions for Class 11 Chemistry**

**Chapter 1-Some basic concepts of chemistry**

**NCERT Solutions for Class 11 Biology**

**NCERT solutions for class 12 maths**

Chapter 1-Relations and Functions | Chapter 9-Differential Equations |

Chapter 2-Inverse Trigonometric Functions | Chapter 10-Vector Algebra |

Chapter 3-Matrices | Chapter 11 – Three Dimensional Geometry |

Chapter 4-Determinants | Chapter 12-Linear Programming |

Chapter 5- Continuity and Differentiability | Chapter 13-Probability |

Chapter 6- Application of Derivation | CBSE Class 12- Question paper of maths 2021 with solutions |

Chapter 7- Integrals | |

Chapter 8-Application of Integrals |

**Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2**

**Class 12 Maths Important Questions-Application of Integrals**

**Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22**

**Solutions of class 12 maths question paper 2021 preboard exam CBSE Solution**