Vertical and horizontal motion

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SUMMARY

The discussion focuses on the mathematical principles governing vertical and horizontal motion in projectile motion, specifically the use of sine and cosine functions. When analyzing motion at an angle θ, the vertical component is calculated using the sine function, while the horizontal component utilizes the cosine function. This relationship stems from the definitions of these trigonometric functions in a right triangle, where sine represents the ratio of the opposite side to the hypotenuse, and cosine represents the ratio of the adjacent side to the hypotenuse. Understanding these components is crucial for accurately analyzing projectile motion.

PREREQUISITES
  • Understanding of trigonometric functions, specifically sine and cosine.
  • Basic knowledge of projectile motion principles.
  • Familiarity with vector components in physics.
  • Ability to analyze right triangles in mathematical contexts.
NEXT STEPS
  • Study the derivation of projectile motion equations using sine and cosine.
  • Learn about vector decomposition in physics.
  • Explore the effects of gravity on vertical motion in more complex scenarios.
  • 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 mathematical foundations of projectile motion.

bobsmith76
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When calculating vertical motion at an angle you use sin, when horizontal you use cos, I don't understand why.
 
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If a velocity is at some angle θ to the horizontal, you must find its vertical and horizontal components. You do that with a bit of trig.
 
I know that but why?
 
bobsmith76 said:
I know that but why?
When analyzing projectile motion, it's often helpful to treat the vertical and horizontal motions separately. The horizontal motion has constant speed, while the vertical motion has constant acceleration.
 
I know that. I'm worried about why is sin paired to vertical and cos paired to horizontal.
 
bobsmith76 said:
I know that. I'm worried about why is sin paired to vertical and cos paired to horizontal.
It has to do with the definitions of those trig functions for a right triangle. For example, the sin function is opposite side over hypotenuse. Since θ is measured from the horizontal, the 'opposite' side will be the vertical component.

For more on finding components, read this: Finding the Components of a Vector
 
ok, that makes more sense, thanks
 
Trigonometry_triangle.jpg

The overall motion will be the longest side, the hypotenuse. This means up is the opposite, and across the the adjacent.
sinx=Opp/Hyp so Opp=sinx*Hyp so up=sinx*speed
in the same way,
cosx=Adj/Hyp so Adj=cosx*Hyp so across=cosx*speed
 

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