Inelastic collision at an angle

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Homework Help Overview

The discussion revolves around determining the angle theta with respect to north made by the velocity vector of two cars after an inelastic collision. The problem involves concepts from momentum conservation and vector decomposition in a two-dimensional context.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants are discussing the relationship between the final velocities of the cars and the angle theta, with references to trigonometric functions. There is an exploration of momentum equations in both x and y directions, and some participants are questioning the correctness of their equations and assumptions regarding the components of velocity.

Discussion Status

There are various attempts to express the angle theta in terms of the given variables, with some participants providing equations for momentum components. However, there is no explicit consensus on the correct approach or solution, and multiple interpretations of the problem are being explored.

Contextual Notes

Participants note the importance of considering the direction of momentum components, particularly the negative y-component for one of the cars. There is also mention of needing to express the final speed in terms of the angle phi, indicating potential constraints in the problem setup.

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Homework Statement


What is the angle theta with respect to north made by the velocity vector of the two cars after the collision?
Express your answer in terms of phi. Your answer should contain an inverse trigonometric function.
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the cars are both of mass m.

Homework Equations


I already found v_final for the first part of the question. The hint says that tan theta = v_final in the x direction / v_final in the y direction.

The Attempt at a Solution



This equation is wrong: (m(2v)+m(v)sin(phi))/(2mv_final cos(theta)) = tan(theta)
 
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Write the momentum equations in x and y.

Note that the y-component of momentum of the car at an angle is negative (opposite) that of the car traveling north at 2v.
 
For x I have v_finalx = (2m)v_final * cos (phi). For y i have v_finaly = (2m)v_final * sin (phi). This would mean that tan (theta) = cos (phi)/sin(phi). I've already tried atan (cos(phi)/sin(phi).
 
how do i do the first part?
my question is asking me the speed of v_final

i think its sqrt ( (v_final * cos (phi))^2 + (2v_final - v_final * sin (phi) ) ^2 )
 

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