Range of projectile traveling through two points at same elevation

AI Thread Summary
The discussion focuses on the calculations related to a projectile fired at an initial velocity V_o that passes through two points at the same elevation, both a distance h above the horizontal. Participants debate the relationship between the height h and the horizontal distance A, questioning the use of tan(45) in their equations. Clarifications are made regarding the correct expressions for h and A, emphasizing the need to express h in terms of A to analyze the maximum range of the projectile. The conversation highlights the importance of accurately defining variables and equations in projectile motion problems. Overall, the thread seeks to resolve the mathematical relationships governing projectile trajectories at equal elevations.
UrbanXrisis
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"A projectile is fired with an initial velocity V_o such that it passes through two points both a distant h above the horizontal. Show that if the gun is adjusted for a maximum range the separation of the potins is?"

my work is http://home.earthlink.net/~suburban-xrisis/projectile.pdf"

does it look correct?
 
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h/A does NOT equal tan 45. Just look at your picture to see this.
Find h in terms of A by using the eqs. A=v_0 t cos45 and
h=v_0 t sin45-(1/2)gt^2.
 
I'm not sure why they would not be equal.

Opposite/Adjacent = tan(theta)

The side opposite to the angle is h
The side Adjacent to the angle is A

so the equation should read: tan(45)=h/A

and why would I want to get h in terms of A? Dont I want A in terms of h?

I made up the variable A so I that I could get A in terms of h and subtract it from the max range.
 
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