How Are Vertical Distances Calculated in Projectile Motion?

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SUMMARY

The discussion focuses on the calculation of vertical distances in projectile motion, specifically using the equations of motion. The key equation presented is h = y + xtan(30), where h represents the vertical distance, y is the initial vertical position, and x is the horizontal distance. The vertical motion is analyzed using the equation s = ut + 1/2at², where s is distance, u is the initial vertical velocity, and a is the acceleration due to gravity. Participants seek clarification on deriving these equations and understanding the initial vertical velocity and acceleration in the context of a skier's motion.

PREREQUISITES
  • Understanding of basic physics concepts, particularly projectile motion.
  • Familiarity with the equations of motion, specifically s = ut + 1/2at².
  • Knowledge of trigonometric functions, particularly tangent.
  • Basic calculus for differentiation in motion analysis.
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  • Study the derivation of projectile motion equations, focusing on vertical and horizontal components.
  • Learn about the role of initial velocity in projectile motion calculations.
  • Explore the effects of gravity on vertical motion and how it influences trajectory.
  • Investigate the application of calculus in optimizing projectile motion problems.
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Students of physics, educators teaching projectile motion, and anyone interested in the mathematical modeling of motion in sports or engineering contexts.

salman213
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I get (a) part but for the last part to find the vertical distances can someone explain what is done here. This is the solution

let h be the vertical distance

h = y + xtan30

h= volt tan30 - 1/2gt^2

then they differentiate to find maximum (i get that part). I just don't understand how they came up with those equations for the h distance...

can anyone explain?
 
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One of the equations of motion s = ut + 1/2at^2
Where s is distance, u is initial velocity, a is accelaration.
If you only think about the vertical motion of the skier, what is the initial vertical velocity and what is the accelaration.
 

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