Projectile Motion inquiry (1 Viewer)

[ajtho777]

Hi y'all, I've been going over some projectile motion.

Since we define y = -1/2(g)t^2 +Vtsinθ and x = Vtcosθ, which can be converted from parametric to cartesian form. But what is the significance of dy/dx? Does it represent the ratio at which the change in y occurs over the change in x? Or is there some other meaning to?

 

[liamkk112]

Hi y'all, I've been going over some projectile motion.

Since we define y = -1/2(g)t^2 +Vtsinθ and x = Vtcosθ, which can be converted from parametric to cartesian form. But what is the significance of dy/dx? Does it represent the ratio at which the change in y occurs over the change in x? Or is there some other meaning to?

dy/dx (x) represents the gradient of the tangent line to the projectile's path at x. it's just like the regular derivative

 

[wizzkids]

dy/dx (x) is proportional to the magnitude of instantaneous vertical component of velocity of the projectile. It will have a magnitude of zero at the point of inflection when the projectile achieves it's maximum altitude.