Hi, I'm reading about particle disintegration at the moment and there's a step I don't follow.(adsbygoogle = window.adsbygoogle || []).push({});

I've got the following equation:

[tex]\tan\theta=\frac{v_0\sin\theta_0}{v_0\cos\theta_0+V} [/tex] where [tex] \theta [/tex] is the resultant angle in the Laboratory system and [tex] \theta_0 [/tex] is the resultant angle in the Centre of Mass system.

Also given is [tex]v=V+v_0[/tex] which are respectively the velocity of a resulting particle in the L system, the velocity of the primary particle in the L system, and the velocity of the resulting particle in the C system.

Solving for [tex]\cos\theta_0[/tex] one should obtain

[tex]\cos\theta_0=-\frac{V}{v_0}\sin^2\theta \pm \cos\theta\sqrt{1-\frac{V^2\sin^2\theta}{v_0^2}}[/tex]

but I've gotten [tex]\cos\theta_0=\frac{V}{v_0}(\cos\theta-1)+\cos\theta[/tex]

from the substitution [tex]\sin\theta_0=\sin\theta\left(\frac{V+v_0}{v_0}\right)[/tex] which seems geometrically sound.

Can anyone see where that other equation comes from for [tex]\cos\theta_0[/tex]?

Thanks.

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# Homework Help: Particle Disintegration: Equation trouble

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