# UCLA prof is killing me with this derivation! help!

## Homework Statement

This is for calc based physics, and the new phs prof wants us to derive this equation for a projectile motion lab.

From this range equation: R(theta) = (v_o^2cos(theta) / g) * [sin(theta) + $$\sqrt{sin^2(theta+ (2gh/v_o^2}$$]

he wants us to derive this range maximizing equation: (theta)=cot^-1$$\sqrt{}1 + (2gh/v_o^2)$$

## The Attempt at a Solution

I was able to differentiate the inside of the sqrrt to 1 + 2gh/v_o^2 , because I made sin^2(theta) = to p and that just differentiated to 1, but how the heck do you get cot^-1???

also, another thing that is throwing me off is the fact that g(gravity) is a constant, so won't that just go to 0? but if that happens then the range eqution can't be differentiated...right?

SammyS
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Homework Helper
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## Homework Statement

This is for calc based physics, and the new phs prof wants us to derive this equation for a projectile motion lab.

From this range equation: R(theta) = (v_o^2cos(theta) / g) * [sin(theta) + $$\sqrt{sin^2(theta+ (2gh/v_o^2}$$]

he wants us to derive this range maximizing equation: (theta)=cot^-1$$\sqrt{}1 + (2gh/v_o^2)$$

## The Attempt at a Solution

I was able to differentiate the inside of the sqrt to 1 + 2gh/v_o^2 , because I made sin^2(theta) = to p and that just differentiated to 1, but how the heck do you get cot^-1???

also, another thing that is throwing me off is the fact that g(gravity) is a constant, so won't that just go to 0? but if that happens then the range equation can't be differentiated...right?

ALSO: if $$\theta = \cot^{-1}\sqrt{1 + (2gh/{v_0}^2)}$$, that means $$\cot(\theta) = \sqrt{1 + (2gh/{v_0}^2)}$$