Spontaneous disintegration in classical mechanics

[ilp89]

Could someone demonstrate to me how in Landau's Mechanics book, he gets from equation (16.5)

tan θ = (v_0 sin θ_0) / (v_0 cos θ_0 + V)

to equation (16.6)

cos θ_0 = -(V/v_0) sin^2 θ ± cos θ √[1 - (V/v_0)^2 sin^2 θ]

I am using the quadratic formula, and the first term on the right comes out fine, but I can't get the second term.

Thanks!

 

[vela]

It worked out for me. What did you get for the quadratic you needed to solve and what did you get for the discriminant?

 

[genericusrnme]

Oh boy, I remember doing that one
a lot of the equations in those books are quite annoying (not 'hard' exactly) to arrive at.
you just need to make use of [itex]sin=\sqrt{1-cos^2}[/itex]

there are a lot more tricky ones later on though so good luck