# Titled reference frame, N2L with position and velocity

by Oblio
Tags: frame, position, reference, titled, velocity
 P: 397 i have a feeling this is wrong for dy....
HW Helper
P: 4,124
 Quote by Oblio i have a feeling this is wrong for dy....
Looks right to me. So now you want to find the range...
 P: 397 range?
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P: 4,124
 Quote by Oblio range?
the question asks for the range...
 P: 397 which is really just the displacement up the plane?
HW Helper
P: 4,124
 Quote by Oblio which is really just the displacement up the plane?
yes, maximum displacement... the object is thrown at an angle, then hits the incline eventually... the displacement up the plane when it hits is the range...
 P: 397 is this the same kinematics equation?
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P: 4,124
 Quote by Oblio dx = vocos$$\vartheta$$t + (1/2)(-g)t^2sin$$\phi$$ dy = vosin$$\vartheta$$t + (1/2)(-g)t^2cos$$\phi$$
use these equations to find dx when dy = 0... that gives the range.
 P: 397 solve for...... vo? and insert into dx?
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P: 4,124
 Quote by Oblio solve for...... vo? and insert into dx?
no, you want to eliminate t... so solve for t and substitute into dx.
 P: 397 without simplifying yet.. dx = vocos (theta) (vosin (theta) / (-1/2)gsin(phi)) + (1/2)(-g)cos(phi)((vosin(theta)/(-1/2)gsin)^2) ya?
HW Helper
P: 4,124
 Quote by Oblio without simplifying yet.. dx = vocos (theta) (vosin (theta) / (-1/2)gsin(phi)) + (1/2)(-g)cos(phi)((vosin(theta)/(-1/2)gsin)^2) ya?
hmm... close but some mistakes... can you post what you got for t?
 P: 397 t = vosin(theta) / (-1/2)gsin(phi)
HW Helper
P: 4,124
 Quote by Oblio t = vosin(theta) / (-1/2)gsin(phi)
setting dy = 0, and solving for t will give you something different... it should be cos(phi) and the - shouldn't be there.
 P: 397 oops! little pen and ink mistake over here.. t = vosin(theta) / (1/2)gcos(phi) yep!
HW Helper
P: 4,124
 Quote by Oblio oops! little pen and ink mistake over here.. t = vosin(theta) / (1/2)gcos(phi) yep!
cool. plugging that into dx should work.
 P: 397 dx = vocos(theta)vosin(theta)/(1/2)gcos(phi) - (1/2)gsin(phi)vosin(theta)/(1/2)gcos(phi)
HW Helper
P: 4,124
 Quote by Oblio 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.

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