Example 5: Horizontal Distance Traveled by a Projectile

https://3speak.tv/watch?v=mes/8dbed9fa In this video, I determine the vector formula for path of a projectile launched at an angle by integrating the acceleration due to gravity acting on it, and then integrating its velocity vector. When the y-component of the position vector is equal to zero (i.e. the object strikes the ground), the corresponding non-trivial time variable corresponds to the horizontal distance traveled. This distance is maximized when the launch angle is π/4 radians or 45 degrees. #math #vectors #calculus #physics #education Timestamps: Example 5: Find angle that gives the maximum horizontal distance traveled by a projectile – 0:00 Solution: Gravity is the only force that acts on the object – 0:49 Integrate the acceleration due to gravity to get the velocity vector – 3:02 Integrate the velocity vector to obtain the position vector – 5:29 Components of the initial velocity – 8:04 Position vector and the parametric equations of trajectory – 11:00 The projectile follows the path of a parabola since y is a quadratic function of x – 13:39 Horizontal distance is the value of x when y = 0 – 16:23 Solving for the distance by plugging in the non-trivial t-value associated with y = 0 – 18:57 Recall the sine double-angle formula – 21:17 The distance is maximum when the launch angle is 45 degrees of π/4 radians – 21:42 Notes and playlists: 3Speak: Summary: https://inleo.io/threads/view/mes/re-leothreads-ise7bvlp Hive Notes: https://peakd.com/hive-128780/@mes/e443f9d3 Sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0Hxo8aPU3ezG0tcLvgJnxLB . Become a MES Super Fan! https://www.youtube.com/channel/UCUUBq1GPBvvGNz7dpgO14Ow/join DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate SUBSCRIBE via EMAIL: https://mes.fm/subscribe MES Links: https://mes.fm/links MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes Email me: [email protected] Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps