Uploaded May 2026 | Updated September 2026, 2 weeks ago
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: 3speak.tv/watch?v=mes/ae000ba6
- Summary: inleo.io/threads/view/mes/re-leothreads-2bhxwpddd
- Hive Notes: peakd.com/hive-128780/@mes/e443f9d3
- Sections playlist: youtube.com/playlist?list=PLai3U8-WIK0Hxo8aPU3ezG0tcLvgJnxLB .
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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: 3speak.tv/watch?v=mes/ae000ba6
- Summary: inleo.io/threads/view/mes/re-leothreads-2bhxwpddd
- Hive Notes: peakd.com/hive-128780/@mes/e443f9d3
- Sections playlist: youtube.com/playlist?list=PLai3U8-WIK0Hxo8aPU3ezG0tcLvgJnxLB .
------------------------------------------------------
Become a MES Super Fan! 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: peakd.com/@mes
Email me: contact@mes.fm
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
