Projectile aimed at a target downrange will always hit when dropped and fired at the same time!
https://play.3speak.tv/embed?v=mes/56y6ngb2
In this video, I show that firing a projectile while aiming at a distance target downrange and dropping it at the same time will always cause the projectile to hit the target, provided that the projectile doesn't hit the ground before reaching the target. This is because both the projectile and object accelerate downwards at the same rate due to gravity, and this is represented in the (-1/2)gt² term of the y-component in the parametric equations of projectile motion. This result is pretty amazing, and allows for some pretty cool stunts and trick shots to attempt!
Notes - 3Speak - YouTube - Telegram - Problems Plus - https://mes.fm/math
#math #calculus #vectorfunctions #problemsplus #projectilemotion
Timestamps
- Problem (c): Projectile always hits dropped target – 0:00
- Solution: Gun is aimed at a target downrange that is dropped when fired – 1:33
- Obtaining our parametric equations of projectile motion at x = D – 4:26
- Target falls at the same rate due to gravity as the projectile – 6:34
- Projectile always hits the target! – 8:34
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