theorem 20.2 Parabolic trajectory

open in the book · parts/03-classical-mechanics/03-exp-projectile-motion.tex:85 · p. 764

Rests on

depends_on equation 18.7 eq:kin-const-acc-itinerary ¶
depends_on phenomenon 20.1 phen:parabolic-trajectory ¶
- depends_on equation 18.7 eq:kin-const-acc-itinerary ¶ ↺
- depends_on phenomenon 18.12 Uniformly accelerated motion ¶
  - depends_on definition 18.11 Acceleration ¶
    - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on definition 18.10 Velocity ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶ ↺
      - depends_on definition 18.9 Position ¶
      - depends_on definition 13.9 Tangent vector to a curve ¶
  - depends_on equation 18.7 eq:kin-const-acc-itinerary ¶ ↺
  - proves proof ch:01-kinematics@proof-1 ¶
depends_on postulate 19.8 Newton's second law ¶
- depends_on definition 19.5 Linear momentum ¶
  - depends_on definition 18.10 Velocity ¶ ↺
  - depends_on definition 19.3 Mass ¶
    - depends_on definition 18.3 Particle ¶
    - depends_on postulate 19.1 Inertia ¶
      - depends_on definition 18.8 Inertial frame of reference ¶
      - depends_on definition 18.3 Particle ¶ ↺
- depends_on postulate 19.6 Newton's first law ¶
  - depends_on definition 18.8 Inertial frame of reference ¶ ↺
  - depends_on definition 19.5 Linear momentum ¶ ↺
proves proof ch:03-exp-projectile-motion@proof-1 ¶

Supports

depends_on corollary 20.3 Range, apex, time of flight ¶
- depends_on example 20.4 ex:projectile-everyday ¶
- depends_on phenomenon 20.6 Air drag ¶
- depends_on proposition 20.9 Linear resistance: exact motion, and the lost range ¶
  - depends_on remark 20.11 What has no closed form, and what to do about it ¶
depends_on phenomenon 20.6 Air drag ¶ ↺
depends_on remark 20.5 rem:projectile-idealisation ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	eq:kin-const-acc-itinerary	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:95
`depends_on`	→	phen:parabolic-trajectory	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:95
`depends_on`	→	Newton's second law	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:95
`depends_on`	←	Range, apex, time of flight	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:193
`depends_on`	←	Air drag	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:434
`depends_on`	←	rem:projectile-idealisation	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:234
`proves`	←	ch:03-exp-projectile-motion@proof-1	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:99