Uploaded May 2026 | Updated September 2026, 3 weeks ago
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: 3speak.tv/watch?v=mes/8dbed9fa
- Summary: inleo.io/threads/view/mes/re-leothreads-ise7bvlp
- 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 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: 3speak.tv/watch?v=mes/8dbed9fa
- Summary: inleo.io/threads/view/mes/re-leothreads-ise7bvlp
- 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
