Vertical and horizontal motion

[bobsmith76]

When calculating vertical motion at an angle you use sin, when horizontal you use cos, I don't understand why.

 

[Doc Al]

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.

 

[bobsmith76]

I know that but why?

 

[Doc Al]

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.

 

[bobsmith76]

I know that. I'm worried about why is sin paired to vertical and cos paired to horizontal.

 

[Doc Al]

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

 

[bobsmith76]

ok, that makes more sense, thanks

 

[jetwaterluffy]

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