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Envelope of the Trajectories with the same Velocity of Projection

Lesson 117 of 135 • 0 upvotes • 5:17mins

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Asim Anand

Enveloping Parabola.

Mathematics Optional for UPSC - Dynamics

135 lessons • 9h 47m

1

Overview

1:42mins

2

Kinematics in Two Dimensions - I [Chapter 1]

10:33mins

3

Kinematics in Two Dimensions - II

9:50mins

4

Kinematics in Two Dimensions - III

10:56mins

5

Kinematics in Two Dimensions - IV

8:45mins

6

Solved Examples - I

9:52mins

7

Solved Examples - II

11:19mins

8

Solved Examples - III

12:40mins

9

Radial and Transverse Velocities

4:53mins

10

Radial and Transverse Accelerations

2:35mins

11

Solved Examples

4:30mins

12

Tangential and Normal Velocities

6:24mins

13

Tangential and Normal Accelerations

3:17mins

14

Solved Examples [Chapter 1 conclusion]

2:43mins

15

Rectilinear Motion - Introduction [Chapter 2]

6:32mins

16

Solved Examples

6:12mins

17

Motion under Constant Acceleration

4:12mins

18

Solved Examples

9:51mins

19

Newton's Laws of Motion

3:14mins

20

Simple Harmonic Motion (S.H.M.) - Introduction

10:29mins

21

S.H.M. - Nature of motion

4:33mins

22

S.H.M. - Important Definitions

9:26mins

23

Geometrical Representation of S.H.M.

5:23mins

24

Important results about S.H.M.

2:17mins

25

Solved Examples

13:24mins

26

Hooke's Law

5:11mins

27

Horizontal Elastic String - Equations of Motion

5:32mins

28

Horizontal Elastic String - Character of Motion

6:09mins

29

Solved Example

6:59mins

30

Vertical Elastic String - Equations of Motion

7:10mins

31

Vertical Elastic String - Two important cases

7:27mins

32

Solved Examples

11:24mins

33

Correction

0:32mins

34

Motion under Inverse Square Law

7:53mins

35

Newton's Law of Gravitation

1:25mins

36

Solved Examples

9:49mins

37

Motion under Miscellaneous Laws of Forces [Chapter 2 conclusion]

7:22mins

38

Constrained Motion - Motion in a Vertical Circle [Chapter 3]

11:09mins

39

Motion in a Vertical Circle - Case I

1:59mins

40

Motion in a Vertical Circle - Case II

1:21mins

41

Motion in a Vertical Circle - Case III

2:47mins

42

Motion in a Vertical Circle - Case IV

3:32mins

43

Important Results from Projectiles

3:59mins

44

Solved Examples

5:38mins

45

Motion on the Outside of a smooth Vertical Circle

10:30mins

46

Solved Examples

6:28mins

47

Cycloid

4:37mins

48

Motion on a Cycloid - I

5:44mins

49

Motion on a Cycloid - II

3:33mins

50

Solved Examples

4:44mins

51

Motion on the outside of a smooth Cycloid

5:25mins

52

Solved Examples

14:31mins

53

Simple Pendulum - Introduction

2:40mins

54

Simple Pendulum - Small Oscillations

1:10mins

55

Simple Pendulum - Oscillations are not small

5:24mins

56

Beats and Second's Pendulum

2:35mins

57

Gain or Loss of Beats

4:41mins

58

Gain or loss of beats - Specific Situations

4:18mins

59

Solved Example [Chapter 3 conclusion]

2:14mins

60

Central Orbits - Introduction [Chapter 4]

5:56mins

61

Differential Equation of a Central Orbit - Polar Form

5:26mins

62

Differential Equation of a Central Orbit - Pedal Form

4:37mins

63

Rate of Description of the Sectorial Area

8:51mins

64

Elliptic Orbit - Law of Force

3:16mins

65

Elliptic Orbit - Velocity at any point

2:12mins

66

Elliptic Orbit - Periodic Time

2:37mins

67

Hyperbolic & Parabolic Orbits

2:05mins

68

Velocity from Infinity

2:45mins

69

Velocity in a Circle

2:31mins

70

Given the Central Orbit, to find the Law of Force

2:27mins

71

Solved Examples

6:56mins

72

Apse, Apsidal Distance & Apsidal Angle

3:15mins

73

Theorem

3:03mins

74

Given the Law of Force, to find the Orbit

1:29mins

75

Solved Examples [Chapter 4 conclusion]

10:55mins

76

Planetary Motion - Newton's Law of Gravitation [Chapter 5]

1:27mins

77

Motion under the Inverse Square Law

3:29mins

78

Elliptic, Parabolic & Hyperbolic Paths

2:18mins

79

Summary of the three cases

4:49mins

81

Kepler's Laws of Planetary Motion

0:52mins

82

Deductions from Kepler's Laws

2:28mins

83

Important Geometrical Properties of an Ellipse

2:42mins

84

Solved Examples

9:55mins

85

Time of description of an arc - Parabolic Orbit

3:30mins

86

Time of description of an arc - Elliptic Orbit

5:11mins

87

Time of description of an arc - Hyperbolic Orbit [Chapter 5 conclusion]

3:59mins

88

Motion in a Resisting Medium - Introduction [Chapter 6]

1:43mins

89

Terminal Velocity

2:14mins

90

Motion of a Particle falling under Gravity - Relation between v & x

4:25mins

91

Motion of a Particle falling under Gravity - Relation between v & t

2:14mins

92

Motion of a Particle falling under Gravity - Relation between x & t

1:16mins

93

Motion of a Particle Projected Vertically Upwards

5:41mins

94

Solved Examples [Chapter 6 conclusion]

6:10mins

95

Projectile Motion - Introduction [Chapter 7]

1:05mins

96

Motion of a Projectile & it's Trajectory - I

5:32mins

97

Motion of a Projectile and it's Trajectory - II

2:04mins

98

Latus Rectum of the Trajectory

2:45mins

99

Vertex & Focus of the Trajectory

3:29mins

100

Directrix of the Trajectory

1:30mins

101

Time of Flight

1:43mins

102

Horizontal Range

0:57mins

103

Maximum Horizontal Range

3:29mins

104

Maximum Height

0:59mins

105

Velocity at any point of the Trajectory

3:10mins

106

Locus of the Focus of the Trajectory

1:55mins

107

Locus of the Vertex of the Trajectory

1:22mins

108

Important Geometrical Properties of a Parabola

2:11mins

109

Solved Examples

5:40mins

110

Two directions of projection to hit a given point

1:38mins

111

Least velocity of projection to hit a given point

2:30mins

112

Two times of flight to hit a given point

2:13mins

113

Range and Time of Flight on an Inclined Plane

5:20mins

114

Maximum Range up the Inclined Plane

5:14mins

115

Range & Time of Flight down an Inclined Plane

5:16mins

116

Solved Examples

4:29mins

117

Envelope of the Trajectories with the same Velocity of Projection

5:17mins

118

Geometrical Interpretation of the Enveloping Parabola & Solved Example

5:21mins

119

Particles suffered to describe Parabolic Paths & Solved Example [Chapter 7 conclusion]

6:16mins

120

Work - I [Chapter 8]

5:17mins

121

Work - II

6:09mins

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