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Maximum range problem, please help!

by delve
Tags: maximum, range
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delve
#1
Feb28-12, 03:50 PM
P: 34
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
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tiny-tim
#2
Feb28-12, 04:17 PM
Sci Advisor
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tiny-tim's Avatar
P: 26,148
Hey David!
Quote Quote by delve View Post
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
#3
Feb28-12, 10:06 PM
P: 34
Thank you very much Tiny-Tim! That was exactly what I needed! :D


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