- #36
Oblio
- 398
- 0
dx = vocos[tex]\vartheta[/tex]t + (1/2)(-g)t^2sin[tex]\phi[/tex]
dy = vosin[tex]\vartheta[/tex]t + (1/2)(-g)t^2cos[tex]\phi[/tex]
dy = vosin[tex]\vartheta[/tex]t + (1/2)(-g)t^2cos[tex]\phi[/tex]
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Oblio said:i have a feeling this is wrong for dy...
Oblio said:range?
Oblio said:which is really just the displacement up the plane?
Oblio said:dx = vocos[tex]\vartheta[/tex]t + (1/2)(-g)t^2sin[tex]\phi[/tex]
dy = vosin[tex]\vartheta[/tex]t + (1/2)(-g)t^2cos[tex]\phi[/tex]
Oblio said:solve for... vo? and insert into dx?
Oblio said:without simplifying yet..
dx = vocos (theta) (vosin (theta) / (-1/2)gsin(phi)) + (1/2)(-g)cos(phi)((vosin(theta)/(-1/2)gsin)^2)
ya?
Oblio said:t = vosin(theta) / (-1/2)gsin(phi)
Oblio said:oops! little pen and ink mistake over here..
t = vosin(theta) / (1/2)gcos(phi)
yep!
Oblio said:dx = vocos(theta)vosin(theta)/(1/2)gcos(phi) - (1/2)gsin(phi)vosin(theta)/(1/2)gcos(phi)
Oblio said:dx = vocos(theta)vosin(theta)/(1/2)gcos(phi) - (1/2)gsin(phi)(vosin(theta)/(1/2)gcos(phi))^2
on the right side i can cancel out the (1/2) on the bottom and top, as well as the g, giving,
dx = vocos(theta)vosin(theta)/(1/2)gcos(phi) - sin(phi)(vosin(theta)/cos(phi))^2
Oblio said:oops again.
so I am left with
dx = vocos(theta)vosin(theta)/(1/2)gcos(phi) - sin(phi)(vo^2 sin(theta) ^2 / (1/2) g (cos(phi)^2)
Oblio said:im confused how one would ever get, for example : cos (theta + phi) through simplifying
Oblio said:i found that cos (a+b) = cosacosb +/- sinasinb... but i don't have that relationship anywhere
Oblio said:k I am at
dx= vo^2sin(theta)*(cos(theta)-sin(phi)) / (1/2)cos(phi)^2(sin(theta))
Oblio said:i can't factor out a vo^2?
Oblio said:i edited that in by mistake. i meant to put that in the numerator.
dx= vo^2sin(theta)*(cos(theta)-sin(phi)sin(theta) / (1/2)gcos(phi)^2