Search 6,000+ CA Community College Courses
Applications of Calculus to Mechanics

Applications of Calculus to Mechanics

Eddie Woo via YouTube Direct link

Application of Projectile Motion (4 of 4: Proving that Path taken by projectile is a parabola)

112 of 194
Previous
Next

112 of 194

Application of Projectile Motion (4 of 4: Proving that Path taken by projectile is a parabola)

Class Central Classrooms beta

YouTube videos curated by Class Central.

Classroom Contents

Applications of Calculus to Mechanics

Automatically move to the next video in the Classroom when playback concludes
  1. 1 Functions of Displacement: Example Question
  2. 2 Functions of Displacement: Harder Example (1 of 3 - Finding v²)
  3. 3 Functions of Displacement: Prologue
  4. 4 Functions of Displacement: Proof 1
  5. 5 Functions of Displacement: Proof 2
  6. 6 Functions of Displacement: Harder Example (2 of 3 - Integrating for x)
  7. 7 Functions of Displacement: Harder Example (3 of 3 - Establishing Domain for v)
  8. 8 Gravity & Escape Velocity (1 of 3)
  9. 9 Gravity & Escape Velocity (2 of 3)
  10. 10 Gravity & Escape Velocity (3 of 3)
  11. 11 Introduction to Simple Harmonic Motion
  12. 12 Simple Harmonic Motion: Basic Equations
  13. 13 Characteristics of Simple Harmonic Motion (1 of 2)
  14. 14 Characteristics of Simple Harmonic Motion (2 of 2)
  15. 15 Simple Harmonic Motion: Amplitude Example
  16. 16 Simple Harmonic Motion: Shifted Centre Example (1 of 2)
  17. 17 Simple Harmonic Motion: Shifting the Centre
  18. 18 Simple Harmonic Motion: Shifted Centre Example (2 of 2)
  19. 19 Projectile Motion: North Korean Tank (1 of 4)
  20. 20 Projectile Motion: North Korean Tank (2 of 4)
  21. 21 Projectile Motion: North Korean Tank (3 of 4)
  22. 22 Projectile Motion: Summary of Equations
  23. 23 Projectile Motion: Glenn Mcgrath (1 of 2)
  24. 24 Projectile Motion: Glenn Mcgrath (2 of 2)
  25. 25 Projectile Motion: North Korean Tank (4 of 4)
  26. 26 Projectile Motion: Colliding Particles (1 of 3)
  27. 27 Projectile Motion: Colliding Particles (2 of 3)
  28. 28 Projectile Motion: Colliding Particles (3 of 3)
  29. 29 Tricky Projectile Question: Different Angles of Projection
  30. 30 Tricky Projectile Question: Equation of Path
  31. 31 Tricky Projectile Question: Restriction on Angles
  32. 32 Interpreting Displacement-Time Graphs
  33. 33 Integrating Motion Equations: The Tennis Ball (1 of 3)
  34. 34 Integrating Motion Equations: The Tennis Ball (2 of 3)
  35. 35 Integrating Motion Equations: The Tennis Ball (3 of 3)
  36. 36 Introduction to Simple Harmonic Motion: Time Equations
  37. 37 Key Illustration for Understanding Simple Harmonic Motion
  38. 38 Physical Models and their Differential Equations
  39. 39 Simple Harmonic Motion Example Question: The Spring
  40. 40 Understanding SHM by examining its graphs
  41. 41 Introductory Guide to Describing Motion
  42. 42 Velocity as a Function of Displacement
  43. 43 Acceleration in terms of Velocity (1 of 2: Review)
  44. 44 Acceleration in terms of Velocity (2 of 2: Derivation & Example)
  45. 45 The Ball & Stone (1 of 2: Finding Time of Collision)
  46. 46 The Ball & Stone (2 of 2: Determining Restriction on V)
  47. 47 Simple Harmonic Not-Motion: Fluctuating Temperature
  48. 48 Projectile Motion: Simple Worked Example (1 of 4: Resolving Initial Velocity)
  49. 49 Projectile Motion: Simple Worked Example (2 of 4: Developing 4 Time Equations)
  50. 50 Projectile Motion: Simple Worked Example (3 of 4: Understanding the Point of Impact)
  51. 51 Projectile Motion: Simple Worked Example (4 of 4: Equation of Path)
  52. 52 Projectile Motion: Aiming for a Target (1 of 2: Generating Time Equations)
  53. 53 Projectile Motion: Aiming for a Target (2 of 2: Determining Firing Angle)
  54. 54 Relationship Between High & Low Firing Angles
  55. 55 Equation of Path Example Question (1 of 2): Identifying Important Features
  56. 56 Equation of Path Example Question (2 of 2): Adding in a Slanted Road
  57. 57 Equation of Path: Understanding Time as the Parameter
  58. 58 Mid-Air Target Question (1 of 4): Time of Equal Horizontal/Vertical Displacement
  59. 59 Mid-Air Target Question (2 of 4): Time of Impact
  60. 60 Mid-Air Target Question (3 of 4): Implied Restriction on Firing Angle
  61. 61 Mid-Air Target Question (4 of 4): Two Final Results
  62. 62 Exam Problem: Simple Harmonic Motion with Auxiliary Angle
  63. 63 Defining Momentum & Force
  64. 64 Introduction to Mechanics
  65. 65 Newton's First Law: Inertia
  66. 66 Mechanics Example 1: Using F = ma to find v(t)
  67. 67 Newton's Second Law: Inertial Mass
  68. 68 Newton's Third Law: Reactions
  69. 69 Mechanics Example 2: Using F = ma to find v(x)
  70. 70 Mechanics Example 3: Starting from Displacement Function
  71. 71 Mechanics Example 4: Calculating Total Distance of a Multi-Step Journey
  72. 72 Weight
  73. 73 Introduction to Resisted Motion (1 of 2: What is Resistance?)
  74. 74 Introduction to Resisted Motion (2 of 2: Example question)
  75. 75 Resistance - should it be kv or mkv? (1 of 3: Introductory thoughts)
  76. 76 Resistance - should it be kv or mkv? (2 of 3: Inferring from details in the question)
  77. 77 Resistance - should it be kv or mkv? (3 of 3: What to do when it's ambiguous)
  78. 78 Vertical Resistance & Gravity example question (1 of 2: Finding x(v))
  79. 79 Vertical Resistance & Gravity example question (2 of 2: Proving Final Result)
  80. 80 Vertical Resistance & Gravity: Framing the Question
  81. 81 Mechanics Example 5: Momentum, Terminal Velocity & Total Distance
  82. 82 Physics vs. "Motion" in Mathematics (1 of 2: What's included?)
  83. 83 Physics vs. "Motion" in Mathematics (2 of 2: What's different?)
  84. 84 Types of Motion in HSC Mathematics (2U, Ext 1 & Ext 2)
  85. 85 Introduction to Simple Harmonic Motion (1 of 2: Key Features)
  86. 86 Introduction to Simple Harmonic Motion (2 of 2: Time Equations)
  87. 87 Simple Harmonic Motion Question (1 of 3: Basic Features)
  88. 88 Simple Harmonic Motion Question (2 of 3: Extreme Values)
  89. 89 Harder SHM Question (1 of 5: Interpreting the question)
  90. 90 Harder SHM Question (2 of 5: Setting up the equations)
  91. 91 Harder SHM Question (3 of 5: Determining specific times)
  92. 92 Simple Harmonic Motion Question (3 of 3: Other Characteristics)
  93. 93 Harder SHM Question (4 of 5: Examining the geometry of movement)
  94. 94 Harder SHM Question (5 of 5: Determining specific speed)
  95. 95 Alternate Forms for Simple Harmonic Motion (Example 1 of 2)
  96. 96 Alternate Forms for Simple Harmonic Motion (Example 2 of 2)
  97. 97 Motion as Functions of Displacement (1 of 2: Why it matters)
  98. 98 Motion as Functions of Displacement (2 of 2: Example question)
  99. 99 Full Derivation of Acceleration = d(½v²)/dx
  100. 100 Using d(½v²)/dx without SHM (1 of 2: Understanding Velocity)
  101. 101 Using d(½v²)/dx without SHM (2 of 2: Reintroducing Time)
  102. 102 Using the d(½v²)/dx result (1 of 2: The vertical spring)
  103. 103 Using the d(½v²)/dx result (2 of 2: Rest Position & Max Speed)
  104. 104 Differential Equations for SHM (1 of 2: A curious pattern)
  105. 105 Differential Equations for SHM (2 of 2: Deriving v²=n²[a²-x²])
  106. 106 Projectile Motion (1 of 5: Defining Conditions for Projectile Motion and how time is built into it)
  107. 107 Projectile Motion (2 of 5: Outlining relationship between Initial v, x and y and projection angle)
  108. 108 Applications of Projectile Motion (1 of 4: Proving that two separate particles collide)
  109. 109 Projectile Motion (3 of 5: Defining the Acceleration, Velocity and Displacement Functions for x & y)
  110. 110 Projectile Motion (4 of 5: Finding max height using vertical velocity and displacement equations)
  111. 111 Projectile Motion (5 of 5: Finding Flight Time, Horizontal Range and Impact speed and angle)
  112. 112 Application of Projectile Motion (4 of 4: Proving that Path taken by projectile is a parabola)
  113. 113 Applications of Projectile Motion (2 of 4: Calculating V2, Collision Time & Place)
  114. 114 Applications of Projectile Motion (3 of 4: Finding the velocity the collision occurs at)
  115. 115 Harder Motion (2 of 2: Finding an expression for particle B to substitute time into to find x)
  116. 116 Harder Projectile Motion (1 of 5: Manipulating Trig Identities and finding time as a function of x)
  117. 117 Harder Projectile Motion (2 of 5: Substituting time expression to find velocity in terms of d)
  118. 118 Harder Projectile Motion (3 of 5: Finding what happens when theta approaches alpha and π/2)
  119. 119 Harder Projectile Motion (4 of 5: Finding a relationship between α & θ using Stationary Point)
  120. 120 Harder Projectile Motion (5 of 5: Using the second derivative to find the minimum value of θ)
  121. 121 Mechanics (1 of 7: Introduction to Forces and Newton's First Law and its relation to Mechanics)
  122. 122 Mechanics (2 of 7: Introduction to Newton's Second Law and Third Law and its relation to Mechanics)
  123. 123 Mechanics (3 of 7: Representing Physical Motion in mathematical terms)
  124. 124 Mechanics (4 of 7: Finding the angle subtended by the other line with the horizontal wall)
  125. 125 Mechanics (5 of 7: Resolving Forces to find the Horizontal forces acting on both strings)
  126. 126 Mechanics (6 of 7: Finding the Forces acting on the particle vertically)
  127. 127 Mechanics (7 of 7: Introductory Example to Mathematical Representation of Physical Motion)
  128. 128 Resisted Motion - Basic Example (1 of 2: Time as a function of Velocity)
  129. 129 Resisted Motion: Introductory Concepts
  130. 130 Resisted Motion - Basic Example (2 of 2: Further Manipulation & Conclusions)
  131. 131 Resisted Motion - Harder Example (1 of 2: Maximum Height)
  132. 132 Resisted Motion - Harder Example (2 of 2: End of the journey)
  133. 133 Intro to Straight Line Motion (1 of 3: Overview of language)
  134. 134 Intro to Straight Line Motion (2 of 3: Unpacking a basic question)
  135. 135 Intro to Straight Line Motion (3 of 3: Interpreting the equations)
  136. 136 Simple Harmonic Motion Example Question (1 of 3: Determining period of motion)
  137. 137 Simple Harmonic Motion Example Question (2 of 3: Solving for time)
  138. 138 Simple Harmonic Motion Example Question (3 of 3: Using graph symmetry)
  139. 139 SHM - Other Centres of Motion (1 of 2: Rearranging with trigonometric identities)
  140. 140 SHM - Other Centres of Motion (2 of 2: Determining attributes from the equation)
  141. 141 Functions of Displacement (1 of 3: Basic Simple Harmonic Motion)
  142. 142 Functions of Displacement (2 of 3: SHM with different centre)
  143. 143 Functions of Displacement (3 of 3: Straight line motion example)
  144. 144 Equation of Path (1 of 4: Establishing the horizontal equations)
  145. 145 Equation of Path (2 of 4: Deriving the Cartesian equation)
  146. 146 Equation of Path (3 of 4: Finding horizontal range)
  147. 147 Equation of Path (4 of 4: Example question)
  148. 148 Simple Harmonic Motion v² Equation (1 of 2: Deriving the result)
  149. 149 Simple Harmonic Motion v² Equation (2 of 2: Example question)
  150. 150 HSC Tide Question (1 of 3: Proving the time equation)
  151. 151 HSC Tide Question (2 of 3: Solving for time)
  152. 152 HSC Tide Question (3 of 3: Leaving the harbour safely)
  153. 153 Intro to Mechanics (1 of 4: Mathematics & physics)
  154. 154 Intro to Mechanics (2 of 4: Equations & kinematics)
  155. 155 Intro to Mechanics (3 of 4: Simple harmonic motion - foundations)
  156. 156 Intro to Mechanics (4 of 4: Basic SHM example)
  157. 157 Simple Harmonic Motion example (1 of 3: Interpreting given data)
  158. 158 Simple Harmonic Motion example (2 of 3: Forming an equation)
  159. 159 Simple Harmonic Motion example (3 of 3: Identifying the time of a given displacement)
  160. 160 Acceleration in terms of displacement (1 of 2: Explanation)
  161. 161 Acceleration in terms of displacement (2 of 2: Worked example)
  162. 162 Simple Harmonic Velocity via Displacement (1 of 2: Equating forms of acceleration)
  163. 163 Simple Harmonic Velocity via Displacement (2 of 2: Worked example)
  164. 164 Objects in Equilibrium (1 of 4: Comparing forces with displacement)
  165. 165 Objects in Equilibrium (3 of 4: Balancing vertical forces)
  166. 166 Objects in Equilibrium (2 of 4: Using trigonometric relationships)
  167. 167 Objects in Equilibrium (4 of 4: Worked exam question)
  168. 168 Concurrent Forces - Non-Equilibrium (2 of 3: Worked example)
  169. 169 Concurrent Forces - Non-Equilibrium (1 of 3: Introduction)
  170. 170 Concurrent Forces - Non-Equilibrium (3 of 3: Finding magnitude & direction)
  171. 171 Horizontal Resisted Motion (1 of 3: Introduction)
  172. 172 Horizontal Resisted Motion (2 of 3: Velocity in terms of displacement)
  173. 173 Horizontal Resisted Motion (3 of 3: Locating eventual resting place)
  174. 174 Plane Braking Model (3 of 3: Resetting the time variable)
  175. 175 Plane Braking Model (2 of 3: Considering reverse thrust)
  176. 176 Plane Braking Model (1 of 3: Constant frictional force)
  177. 177 Vertical Resisted Motion (5 of 5: How long till it returns to the ground?)
  178. 178 Vertical Resisted Motion (4 of 5: Finding v = f(t) by integration)
  179. 179 Vertical Resisted Motion (3 of 5: Determining the maximum height)
  180. 180 Vertical Resisted Motion (2 of 5: Finding y = f(v) by integration)
  181. 181 Vertical Resisted Motion (1 of 5: Introduction)
  182. 182 Terminal Velocity (1 of 2: Balancing forces)
  183. 183 Terminal Velocity (2 of 2: Determining drop height)
  184. 184 Resisted Projectile Motion (1 of 4: Understanding horizontal motion)
  185. 185 Resisted Projectile Motion (2 of 4: Understanding vertical motion)
  186. 186 Resisted Projectile Motion (3 of 4: Finding cartesian equation)
  187. 187 Resisted Projectile Motion (4 of 4: Determining equations from first principles)
  188. 188 Quadratic Drag (1 of 3: Evaluating the drag coefficient)
  189. 189 Quadratic Drag (2 of 3: Investigating horizontal motion)
  190. 190 Quadratic Drag (3 of 3: Determining the angle of projection)
  191. 191 Proving simple harmonic motion (Exam Question 1 of 10)
  192. 192 Finding maximum speed of SHM (Exam Question 2 of 10)
  193. 193 Forces on a hanging object (Exam Question 5 of 10)
  194. 194 Mechanics of a falling object (Exam Question 10 of 10)

Never Stop Learning.

Get personalized course recommendations, track subjects and courses with reminders, and more.

Sign up for free
Someone learning on their laptop while sitting on the floor.