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Davey Boy
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[EDIT]Title is incorrect, it is a proof using Conservation of Energy/Momentum
You take a pool shot for the win. The perfectly [EDIT]elastic[/EDIT] collision is such that after the collision the Que ball has a non-zero velocity along angle [tex]\theta[/tex], and the 8 ball has a non-zero velocity along angle [tex]\beta[/tex]. Prove that [tex]\theta[/tex]+[tex]\beta[/tex]=90[tex]\circ[/tex]. The two pool balls have exactly the same mass.
No equations are given, but I am fairly certain only [tex]\Delta[/tex]K=[tex]\Delta[/tex]P=0 is needed. My teacher vaguely hinted that those were the equations/principals he recommend we utilize.
I came up with 2 equations:
1) [1/2]M*VIQ2=[1/2]M*VFQ2*cos([tex]\theta)[/tex]+[1/2]M*VF82*cos([tex]\beta[/tex])
2) M*VIQ=M*VIQ*cos([tex]\theta)[/tex]+M*VF8cos([tex]\beta[/tex])
I solved for VFQ and plugged that into the 1st equation. After simplifying I got;
2[(VF8cos([tex]\beta[/tex]))(VFQcos([tex]\theta[/tex]))]=0
I figured out that this means one of those variables must be 0.I know that VFQ is not, and VF8 is not, therefore, one of the angles must be equal to 90[tex]\circ[/tex] for that equation to equal 0.
I believe my initial equations are wrong, though i could have easily made an algebraic mistake. Any pointers would be very nice, Thanks!
Homework Statement
You take a pool shot for the win. The perfectly [EDIT]elastic[/EDIT] collision is such that after the collision the Que ball has a non-zero velocity along angle [tex]\theta[/tex], and the 8 ball has a non-zero velocity along angle [tex]\beta[/tex]. Prove that [tex]\theta[/tex]+[tex]\beta[/tex]=90[tex]\circ[/tex]. The two pool balls have exactly the same mass.
Homework Equations
No equations are given, but I am fairly certain only [tex]\Delta[/tex]K=[tex]\Delta[/tex]P=0 is needed. My teacher vaguely hinted that those were the equations/principals he recommend we utilize.
The Attempt at a Solution
I came up with 2 equations:
1) [1/2]M*VIQ2=[1/2]M*VFQ2*cos([tex]\theta)[/tex]+[1/2]M*VF82*cos([tex]\beta[/tex])
2) M*VIQ=M*VIQ*cos([tex]\theta)[/tex]+M*VF8cos([tex]\beta[/tex])
I solved for VFQ and plugged that into the 1st equation. After simplifying I got;
2[(VF8cos([tex]\beta[/tex]))(VFQcos([tex]\theta[/tex]))]=0
I figured out that this means one of those variables must be 0.I know that VFQ is not, and VF8 is not, therefore, one of the angles must be equal to 90[tex]\circ[/tex] for that equation to equal 0.
I believe my initial equations are wrong, though i could have easily made an algebraic mistake. Any pointers would be very nice, Thanks!
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