Projectile Motion is Symmetric

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SUMMARY

Projectile motion is symmetric in the absence of air resistance, meaning the initial and final velocities are equal in magnitude. A projectile ascending to a zero vertical velocity will descend the same horizontal distance during its downward motion. Understanding this symmetry is crucial, as the time spent moving upwards equals the time spent moving downwards when horizontal velocity remains constant. This relationship between time and distance is fundamental to grasping the concept of projectile motion.

PREREQUISITES
  • Understanding of basic physics concepts, specifically kinematics.
  • Familiarity with the principles of projectile motion.
  • Knowledge of horizontal and vertical velocity components.
  • Basic mathematical skills for calculating time and distance.
NEXT STEPS
  • Study the equations of motion for projectiles in a vacuum.
  • Explore the effects of air resistance on projectile trajectories.
  • Learn about the conservation of energy in projectile motion.
  • Investigate real-world applications of projectile motion in sports and engineering.
USEFUL FOR

Students of physics, educators teaching kinematics, and anyone interested in understanding the principles of motion in a vacuum.

Bashyboy
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Okay, I read that in the case of no air-resistance, projectile motion is symmetric; that the initial velocity will equal the final velocity, in magnitude; and that a projectile traveling upwards, achieving a zero velocity of the vertical component, will have to fall the same horizontal distance during the segment of motion downwards. But, for some odd reason, I just have difficulty grasping this. Is there something I am missing in my understanding? Is there a better way to explain this concept?
 
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Bashyboy said:
Okay, I read that in the case of no air-resistance, projectile motion is symmetric; that the initial velocity will equal the final velocity, in magnitude; and that a projectile traveling upwards, achieving a zero velocity of the vertical component, will have to fall the same horizontal distance during the segment of motion downwards. But, for some odd reason, I just have difficulty grasping this. Is there something I am missing in my understanding? Is there a better way to explain this concept?

I think one way that might help is to understand all of this motion is with relation to time. If something is moving at a constant velocity in the horizontal direction, and it moves in the positive vertical direction for time t, then it will move in the negative direction for time t also. So, if horizontal velocity is constant, and time t up is equal to time t down, then the horizontal distances going up must be the same as down.
 

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