Titled reference frame, N2L with position and velocity

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Homework Help Overview

The discussion revolves around a physics problem involving projectile motion on an inclined plane. The scenario describes a ball thrown with an initial speed at an angle above the incline, requiring the application of Newton's second law to analyze its motion and determine its position over time.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants discuss the setup of the problem, questioning the clarity of the question and the implications of the initial velocity. There are attempts to derive the equations of motion and to understand the components of velocity and acceleration along and perpendicular to the incline.

Discussion Status

The discussion is active, with participants exploring various interpretations of the problem. Some have provided insights into the equations of motion, while others are seeking clarification on the reasoning behind certain steps. There is no explicit consensus, but productive exchanges are occurring regarding the setup and approach to the problem.

Contextual Notes

Participants note potential ambiguities in the problem statement and the need to clarify the definitions of the axes used in the analysis. There is also mention of the importance of distinguishing between the components of motion along the incline and the effects of gravity.

  • #61
im confused how one would ever get, for example : cos (theta + phi) through simplifying
 
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  • #62
Oblio said:
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)...
 
  • #63
i found that cos (a+b) = cosacosb +/- sinasinb... but i don't have that relationship anywhere
 
  • #64
Oblio said:
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.
 
  • #65
k I am at
dx= vo^2sin(theta)*(cos(theta)-sin(phi)) / (1/2)cos(phi)^2(sin(theta))
 
Last edited:
  • #66
Oblio said:
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...
 
  • #67
i can't factor out a vo^2?
 
  • #68
Oblio said:
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
 
  • #69
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
 
  • #70
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

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.
 
  • #71
ya, you mean i didnt multiply it by (1/2)gcos(phi)^2?
 
  • #72
ignore that last one
 

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