Velocity vector along a parabola

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SUMMARY

The discussion centers on the behavior of velocity vectors along a parabolic trajectory, specifically in the context of projectile motion. It is established that the initial and final velocities along the y-axis are equal in magnitude but opposite in direction due to gravitational influence, while the x-axis velocity remains constant. This relationship is derived from Newton's second law, which states that the gravitational force acts solely in the negative y-direction, affecting the velocity accordingly. Understanding these principles is crucial for analyzing motion in a gravitational field.

PREREQUISITES
  • Newton's Second Law of Motion
  • Basic principles of kinematics
  • Understanding of projectile motion
  • Concept of velocity vectors
NEXT STEPS
  • Study the equations of motion for projectile motion
  • Learn about the derivation of velocity vectors in parabolic trajectories
  • Explore the effects of gravitational force on motion
  • Investigate the relationship between initial and final velocities in kinematic equations
USEFUL FOR

Students studying physics, educators teaching kinematics, and anyone interested in understanding the dynamics of projectile motion in gravitational fields.

matatat
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Hello, I'm new here and wasn't sure if this should be put into the homework section. It's not a homework question but the nature of the problem is homework-ish in nature I suppose.

Anyway I'm trying to understand why a velocity vector along a parabola would have the same initial velocity as its final velocity. I realize that velocity along the x-axis is a constant and I think the velocity along the y-axis remains linear. Although I can't figure out why both are so. Could someone explain this to me or direct me to where I would find the answer?

thanks
matt
 
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Sorry also I forgot to mention that it makes sense in the fact that it will have enough velocity to reach a point y and its velocity will be zero and as it returns its velocity will return back to the original but negative. I was more so wondering how I could prove this with kinematics.
 
I assume you're talking about a projectile thrown upwards in a gravitational field, right?

Then the behavior you describe is derived directly from Newton's second law. Namely, the gravitational force only acts in the -y direction. Can you see why this leads to the velocity relationships?
 

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