- #1
bobsmith76
- 336
- 0
When calculating vertical motion at an angle you use sin, when horizontal you use cos, I don't understand why.
Vertical and horizontal motion
- Context: High School
- Thread starter bobsmith76
- Start date
-
- Tags
- Horizontal Motion Vertical
Click For Summary
Discussion Overview
The discussion revolves around understanding the relationship between vertical and horizontal motion in projectile motion, specifically focusing on the use of trigonometric functions (sine and cosine) to resolve velocity into its components. The scope includes conceptual clarification and mathematical reasoning related to the application of trigonometry in physics.
Discussion Character
- Conceptual clarification
- Mathematical reasoning
Main Points Raised
- Some participants express confusion about why sine is associated with vertical motion and cosine with horizontal motion.
- Others explain that to find the vertical and horizontal components of a velocity at an angle θ, trigonometric functions are used, with sine corresponding to the vertical component and cosine to the horizontal component.
- A participant notes that this association is based on the definitions of sine and cosine in relation to a right triangle, where sine represents the opposite side over the hypotenuse and cosine represents the adjacent side over the hypotenuse.
- One participant mentions that analyzing projectile motion separately for vertical and horizontal components is helpful due to the differences in motion characteristics: constant speed in the horizontal direction and constant acceleration in the vertical direction.
Areas of Agreement / Disagreement
Participants generally agree on the use of trigonometric functions to resolve motion into components, but there remains some uncertainty regarding the rationale behind the specific associations of sine and cosine with vertical and horizontal motion.
Contextual Notes
The discussion does not resolve the underlying reasons for the associations of sine and cosine with vertical and horizontal components, and it relies on the definitions of trigonometric functions without delving into potential limitations or assumptions in those definitions.
- #2
Doc Al
Mentor
- 45,583
- 2,457
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.
- #3
bobsmith76
- 336
- 0
I know that but why?
- #4
Doc Al
Mentor
- 45,583
- 2,457
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.bobsmith76 said:
- #5
bobsmith76
- 336
- 0
I know that. I'm worried about why is sin paired to vertical and cos paired to horizontal.
- #6
Doc Al
Mentor
- 45,583
- 2,457
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.bobsmith76 said:
For more on finding components, read this: Finding the Components of a Vector
- #7
bobsmith76
- 336
- 0
ok, that makes more sense, thanks
- #8
jetwaterluffy
- 227
- 0
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
Similar threads
High School
Can energy be decomposed?
- · Replies 2 ·
Undergrad
Lagrangian for pendulum
- · Replies 11 ·
High School
Torsion Involving an Off Axis Thrust
- · Replies 66 ·
- · Replies 3 ·
High School
How to shoot longer shots in basketball
- · Replies 20 ·
- · Replies 10 ·
- · Replies 12 ·
- · Replies 14 ·
- · Replies 15 ·
Undergrad
Momentum of a Water Jet Impacting Plate
- · Replies 1 ·