Just a simple calculus question

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The discussion centers on a calculus question involving projectile motion equations. It explores the manipulation of terms to show the equivalence between two expressions related to the angle of elevation for maximum range when launching from a height. Participants clarify the steps needed to balance the equations, including multiplying and dividing specific terms. The conversation confirms the context of the problem, which involves calculating the optimal angle for maximum range from a cliff. Overall, the thread highlights the mathematical relationships in projectile motion and their applications.
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Why does
((v0^2 sin (2a))/2g) + ((v0 cos a)/g) sqrt(v0^2 ((sin^2)a) +hg) equal
((v0^2 sin (2a))/2g) (1+ sqrt(1+((2hg)/(vo^2) (sin^2)a))) ?
 
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Multiply the right-hand term on the lhs by sin(a) and divide the sq root term by sin²(a) to balance out.
Take out the Vo term from inside the sq root and you should have Vo².sin(2a)/2g as a commom factor.

Let me guess: this to find the angle of elevation for maximum range when firing off a cliff of height h, yes ?
 
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Exactly! Wow thanks a hell of a lot!
 

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