Example 6: Impact Speed of a Projectile Hitting the Ground

https://3speak.tv/watch?v=mes/ae000ba6 In this video, I determine the time a projectile is in the air, the distance it travels, and the speed it impacts the ground after being launched from 10 meters at an angle of 45 degrees and a speed of 150 m/s. I use the parametric equations of trajectory I derived in my earlier video, and set the y component equal to zero to obtain the time when the object hits the ground. Plugging in that specific time value into the x component yields the distance. To get the velocity, we take the derivative of the position vector and then obtain the speed using the same time value, which is 151 m/s, which is similar to the launch speed. #math #vectors #calculus #physics #education Timestamps: Example 6: Find speed a projectile hits the ground – 0:00 Solution: Adjust the parametric equations of trajectory by adding the initial height of launch – 0:40 Plugging in our values into the parametric equations of trajectory – 3:56 Exact trigonometric ratios for π/4 – 6:33 Impact occurs when y = 0, which we can solve for t via the quadratic formula – 9:28 Distance is the x value at y = 0 – 15:03 Calculation check – 16:05 Velocity is the derivative of the position vector – 18:26 Speed at impact is 151 m/s – 21:10 Calculation check – 22:50 Notes and playlists: 3Speak: Summary: https://inleo.io/threads/view/mes/re-leothreads-2bhxwpddd 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