Is Gravity Always Negatively Affecting a Ball?

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SUMMARY

The discussion centers on the analysis of a ball's motion under the influence of gravity, specifically using equations of motion in the xy-plane. Participants derive the components of velocity and acceleration from the parametric equations x=-(5.00m) sin(ωt) and y=(4.00m)-(5.00m)cos(ωt). Key calculations include the derivatives for velocity, x' and y', and acceleration, x'' and y'', confirming that the ball's trajectory resembles a parabolic arc. The conversation emphasizes the importance of unit vectors in representing velocity and acceleration vectors accurately.

PREREQUISITES
  • Understanding of calculus, specifically differentiation and the chain rule.
  • Familiarity with parametric equations in physics.
  • Knowledge of vector notation and unit vectors in two-dimensional motion.
  • Basic concepts of Simple Harmonic Motion (SHM) and its mathematical representation.
NEXT STEPS
  • Study the derivation of parametric equations for motion in two dimensions.
  • Learn about the application of the chain rule in calculus for motion analysis.
  • Explore the concepts of unit vectors and their significance in physics.
  • Investigate the characteristics of trajectories in Simple Harmonic Motion.
USEFUL FOR

Students of physics, particularly those studying mechanics and motion, as well as educators seeking to clarify concepts related to velocity and acceleration in two-dimensional motion.

  • #61
Yea, it seems.
 
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  • #62
Could you check if I did this correct...

The componet for velocity is x’= -(5.00m) ω cos ωt and y’= (5.00m) ω sin ωt
At t=0 seconds, x’= -(5.00m) ω and y’=0m/s
The componet for acceleration is x’’=(5.00m)ω^2 sin ωt and y’’= (5.00m) ω^2 cos ωt
At t=0 seconds, x’’=0m/s^2 and y’’=(5.00m)ω^2
 
  • #63
Looks ok to me.
 
  • #64
I wasnt sure if the omega symbol needed to be included in the answer or not, just checking
 

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