# Titled reference frame, N2L with position and velocity

by Oblio
Tags: frame, position, reference, titled, velocity
 P: 397 oops. man im bad..
 P: 397 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
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P: 4,125
 Quote by 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
careful the 1/2 and g are squared...
 P: 397 oops again. so im left with dx = vocos(theta)vosin(theta)/(1/2)gcos(phi) - sin(phi)(vo^2 sin(theta) ^2 / (1/2) g (cos(phi)^2)
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P: 4,125
 Quote by Oblio oops again. so im 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...
 P: 397 will trig identities apply since theta and phi are present?
 P: 397 im confused how one would ever get, for example : cos (theta + phi) through simplifying
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P: 4,125
 Quote by Oblio 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)...
 P: 397 i found that cos (a+b) = cosacosb +/- sinasinb... but i dont have that relationship anywhere
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P: 4,125
 Quote by Oblio i found that cos (a+b) = cosacosb +/- sinasinb... but i dont 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.
 P: 397 k im at dx= vo^2sin(theta)*(cos(theta)-sin(phi)) / (1/2)cos(phi)^2(sin(theta))
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P: 4,125
 Quote by Oblio k im 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...
 P: 397 i cant factor out a vo^2?
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P: 4,125
 Quote by Oblio i cant 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
 P: 397 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
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P: 4,125
 Quote by 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
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.
 P: 397 ya, you mean i didnt multiply it by (1/2)gcos(phi)^2?
 P: 397 ignore that last one

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