What is the final term in the distance formula for maximum range?

[delve]

Hey guys,

I was hoping somebody might help me; I'm really confused. I obtained the formula for distance, which is this:

d=[(2[v_0]^2(cos[alpha])sin([alpha-beta])]/gcos^2(beta)

And the derivative for distance, which is this:

derivative of d with respect to alpha=0=(2[v_0]^2)/(gcos^2(beta))*(-sin(alpha)sin(alpha-beta)+cos(alpha)cos(alpha-beta))*cos(2alpha-beta)

I was trying to see what alpha would be for maximum range, but I have no idea where the very end term on the right comes from: cos(2alpha-beta). Could somebody please me? Thank you.

David

 

[tiny-tim]

Hey David!

d=[(2[v_0]^2(cos[alpha])sin([alpha-beta])]/gcos^2(beta)

And the derivative for distance, which is this:

derivative of d with respect to alpha=0=(2[v_0]^2)/(gcos^2(beta))*(-sin(alpha)sin(alpha-beta)+cos(alpha)cos(alpha-beta))*cos(2alpha-beta)

No, that *cos(2α-β) at the end must be a misprint for =cos(2α-β) …

cos(A+B) = cosAcosB - sinAsinB ​

 

[delve]

Thank you very much Tiny-Tim! That was exactly what I needed! :D