Problems Plus 1: Projectile fired from the origin
Published on HivePostify by @mes · Thu Sep 03 2026
https://play.3speak.tv/embed?v=mes/51fknkdx
In this video, I examine projectile motion launched from the origin and show that the projectile will always lie within a parabola defined by launching a projectile from the maximum height horizontally at the same initial velocity. I also show that if we are to aim directly at a target downrange and drop the target at the same instance of firing the projectile, then we will always hit our target!
[3Speak](https://3speak.tv/watch?v=mes/problems-plus-1-projectile-813) - [YouTube](https://youtu.be/V4Y5Cp2EAU) - [Telegram](https://t.me/meslinks/35459) - [Notes](https://mes.fm/problems-plus-1-projectile-origin) - [Problems Plus](https://mes.fm/vector-functions-problems-plus) ([Playlist](https://www.youtube.com/playlist?list=PLHNdnBXVWSlo)) - [Vector Functions](https://www.youtube.com/playlist?list=PLai3U8-WIK0HQl7xTQBSO8Te8PcpNm4U) - https://mes.fm/math
#math #calculus #vectorfunctions #problemsplus #projectilemotion
Timestamps
- Problem 1: Projectile fired from the origin – 0:00 - Solution to (a): Angle to achieve maximum height – 2:53 - Maximum height is when the derivative of the position vector = 0 – 3:45 - Time at maximum height – 5:29 - Maximum height is at 90 degrees – 10:00 - Solution to (b): Projectile must stay within this parabola – 10:36 - Recap on the time until a projectile hits the ground – 17:15 - |x| is less than or equal to |R| – 21:21 - Subtracting the projectile path by the formula for the parabola – 30:45 - Difference between the projectile path and parabola is always negative or zero – 37:37 - Obtain a quadratic formula involving the point (a, b) on the projectile path inside or on parabola – 50:35 - Discriminant has to be greater than or equal to zero: 54:15 - The height b satisfies the condition of being on or inside the parabola – 58:08 - Point (a, b) lies on the path of the projectile when tan α satisfies the quadratic formula – 1:03:05 - Solution to (c): Projectile always hits dropped target – 1:04:41 - Launch angle is aimed at target that gets dropped – 1:08:48 - Target falls due to gravity at the same rate as the projectile – 1:12:36 - Projectile always hits the target! – 1:13:22
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--- ▶ [Watch on 3speak.tv](https://3speak.tv/watch?v=mes/problems-plus-1-projectile-813)
Tags: #math#calculus#science#education#projectilemotion#threespeak#vectors#chessbrothers#scifimultiverse#hive-128780