Жүктеп алу "Projectile Motion Using Vector-Valued Functions | Calculus 3 Lesson 38 - JK Math"

How to Solve Projectile Motion Problems Using Vector Functions (Calculus 3 Lesson 38) ➡️ Download my FREE Surfaces Cheat Sheets: https://www.jkmathematics.com//surfaces-cheat-sheets 🖥️ Membership Site (community & bonus content): https://www.jkmathematics.com/plus 🌐 My Website: https://www.jkmathematics.com ⭐️ Support Me on Patreon: https://www.patreon.com/JKMath In this video you will learn about how to solve projectile motion problems using vector functions. In particular, we will derive the formula for the position vector for projectile motion, and then use it solve different scenarios that involve a projectile in motion. This video series is designed to help students understand the concepts of Calculus 3 at a grounded level. No long, boring, and unnecessary explanations, just what you need to know at a reasonable and digestible pace, with the goal of each video being shorter than the average school lecture! Calculus 3 requires a solid understanding of concepts from calculus 2, calculus 1, precalculus, and algebra. This includes limits, differentiation, advanced integration techniques, applications of derivatives and integrals, polar coordinates, parametric equations, trigonometric functions, logarithms, factoring, equation manipulation, graphing, and much more. If you are not familiar with these prerequisite topics, be sure to learn them first! Video Chapters: 0:00 Projectile Motion in Calc 3 6:11 Deriving the Position Vector 22:40 The Position Vector Formula 24:16 Example Part A: When does it land? 31:41 Example Part B: Total Distance 33:20 Example Part C: Maximum Height 37:00 Example Part D: Speed at Impact 39:58 Example Part E: Clear a Fence? 42:20 Example Part F: Tangential Component 📝 Examples Video: https://www.youtube.com/watch?v=Eaq546cvbD4 ⏩ Next Lesson: https://www.youtube.com/watch?v=yf7xUi7r9o0 📺 Calculus 3 Playlist: https://www.youtube.com/playlist?list=PLHdRLeAbIZE5yZ7ydR9qeB_B6CcVFlX63 📺 Calculus 2 Playlist: https://www.youtube.com/playlist?list=PLHdRLeAbIZE7KQ922piyRIDAj30XYcOIu 📺 Calculus 1 Playlist: https://www.youtube.com/playlist?list=PLHdRLeAbIZE6krGDQthaQRpLZFLD4ob54 ⚡️Math Products I Recommend⚡️ Graphing Calculator: https://www.amazon.com/Texas-Instruments-TI-Nspire-Graphing-Calculator/dp/B07RL7HM5V?language=en_US Non-Graphing Calculator: https://www.amazon.com/Texas-Instruments-TI-30X-Scientific-Calculator/dp/B00SWWKEAY?language=en_US Financial Calculator: https://www.amazon.com/s?k=ba+2+plus&language=en_US Graphing Paper: https://www.amazon.com/KAISA-Punched-Loose-Leaf-Binders-150sheet/dp/B096V2RYR2?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&language=en_US College Rule Paper: https://www.amazon.com/Mead-Filler-College-Punched-15326/dp/B000068UWB?language=en_US My Favorite Pencil: https://www.amazon.com/Quick-Mechanical-Pencil-Assorted-Barrel/dp/B07FC5NGBX?language=en_US My Favorite Erasers: https://www.amazon.com/Prismacolor-Premier-Magic-Erasers-3-Count/dp/B005ENNEJW?language=en_US Calculus Workbook: https://www.amazon.com/Essential-Calculus-Practice-Workbook-Solutions/dp/1941691242?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&language=en_US ⚡️Textbooks I Use⚡️ Calculus 1 & 2: https://www.amazon.com/Calculus-Ron-Larson/dp/0547167024?language=en_US Calculus 3: https://www.amazon.com/Multivariable-Calculus-Ron-Larson/dp/1285060296?language=en_US Financial Mathematics: https://www.amazon.com/Mathematics-Investment-Credit-ACTEX-Academic/dp/1566987679?language=en_US Algebra: https://www.amazon.com/Beginning-Algebra-Textbooks-Available-Cengage/dp/1111578702?dib=eyJ2IjoiMSJ9.g0T1GWGzoYKWtGxkj7UalJvCBFYIbNvNGfdeC55goiBg0R4T5OKmBFctoPC2aiQ6TGMfZ0Hgm0kD7yJwMG1IBxaNXWVuU5E8_Z8jzEYNMPoECwTXdNPKeaJHdi6k0nGpwFtaSkDxDCS9ubXCek9laEQflYsOhMfPCarQ6gQPcgAKeyHc79eTbeNCdhsHqz7aRL0gWNzoNN2oMi-fPo9sJ2AMQULppYXjBdAJHry93bCOmjCocOZrI1shLqCMNrQI6eiZUjcHtAALs9aKh21e4IUjdtRa3_3RW8Sg9AJHeyZwUkDBTTtfDvdbvWLDxcYg2vXkdezLVf1Ciixo_feMSNh7oD6w--Iu-TnWEyjxS_2qXvTsTWEN4pQIPq7gZIC26Ncag297fdhehj8oKpt-0bkc1_H1HX8YugHTGDWo4pc7gGIU6IoP1LXDwKlDJRF_.9PoBEP5UOvzmv0NibJkKbRZFnddOsK25HxJ-cGrUg8o&dib_tag=se&language=en_US ⚡️My Recording Equipment⚡️ iPad Air: https://www.amazon.com/Apple-iPad-Air-5th-Generation/dp/B09V3HJBN3?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&th=1&language=en_US Apple Pencil (Gen 2): https://www.amazon.com/Apple-MU8F2AM-A-Pencil-Generation/dp/B07K1WWBJK?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&language=en_US Tablet Desk Stand: https://www.amazon.com/OMOTON-Adjustable-Multi-Angle-Aluminum-Convenient/dp/B015FH0XKE?sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&th=1&language=en_US External Hardrive: https://www.amazon.com/Toshiba-HDTB420XK3AA-Canvio-Portable-External/dp/B079D3D8NR?language=en_US (Commissions earned on qualifying purchases) Follow me on Social Media! https://www.facebook.com/unsupportedbrowser Found this video to be helpful? Consider giving this video a like and subscribing to the channel! Thanks for watching! Any questions? Feedback? Leave a comment! - Josh from JK Mathematics #calculus Disclaimer: Please note that some of the links associated with the videos on my channel may generate affiliate commissions on my behalf. As an amazon associate, I earn from qualifying purchases that you may make through such affiliate links.