Titled reference frame, N2L with position and velocity

[Oblio]

oops! little pen and ink mistake over here..

t = vosin(theta) / (1/2)gcos(phi)
yep!

 

[learningphysics]

oops! little pen and ink mistake over here..

t = vosin(theta) / (1/2)gcos(phi)
yep!

cool. plugging that into dx should work.

 

[Oblio]

dx = vocos(theta)vosin(theta)/(1/2)gcos(phi) - (1/2)gsin(phi)vosin(theta)/(1/2)gcos(phi)

 

[learningphysics]

dx = vocos(theta)vosin(theta)/(1/2)gcos(phi) - (1/2)gsin(phi)vosin(theta)/(1/2)gcos(phi)

you missed t^2... didn't square t.

 

[Oblio]

oops.
man I am bad..

 

[Oblio]

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

 

[learningphysics]

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

careful the 1/2 and g are squared...

 

[Oblio]

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)

 

[learningphysics]

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)

Looks good... try to simplify and use a trig identity to get it to look like the formula they gave for the range...

 

[Oblio]

will trig identities apply since theta and phi are present?

 

[Oblio]

im confused how one would ever get, for example : cos (theta + phi) through simplifying

 

[learningphysics]

im confused how one would ever get, for example : cos (theta + phi) through simplifying

try a little factoring of your equation also... look up the identity for cos(A+B)...

 

[Oblio]

i found that cos (a+b) = cosacosb +/- sinasinb... but i don't have that relationship anywhere

 

[learningphysics]

i found that cos (a+b) = cosacosb +/- sinasinb... but i don't have that relationship anywhere

first write everything over 1 denominator... then compare what you have to the formula you need to get... a little factoring will give you the answer.

 

[Oblio]

k I am at
dx= vo^2sin(theta)*(cos(theta)-sin(phi)) / (1/2)cos(phi)^2(sin(theta))

 

[learningphysics]

k I am at
dx= vo^2sin(theta)*(cos(theta)-sin(phi)) / (1/2)cos(phi)^2(sin(theta))

factoring out the sin(theta) was correct... but you made a mistake somewhere...

 

[Oblio]

i can't factor out a vo^2?

 

[learningphysics]

i can't factor out a vo^2?

yes you can... I was referring to the sin's cos's... check your work... your denominator should only have [cos(phi)]^2

 

[Oblio]

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

 

[learningphysics]

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

almost there... should be cos(theta)cos(phi) in the numerator... I think you forgot to multiply the top by cos(phi) when putting everything over 1 denominator.

 

[Oblio]

ya, you mean i didnt multiply it by (1/2)gcos(phi)^2?

 

[Oblio]

ignore that last one