Proving Projectile Range&Height: Angle of Elevation 30deg vs 60deg

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    Projectile Proof
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A gun will achieve three times the maximum height at a 60-degree angle of elevation compared to a 30-degree angle, while maintaining the same horizontal distance. The equations used for height and range need to be correctly related to demonstrate this relationship. The initial attempt correctly identifies the equations but fails to explicitly prove that the ranges are equal and the heights are proportionally different. To validate the claim, both the height and range must be analyzed separately for each angle. A complete proof requires showing both the equality of ranges and the height ratio.
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Homework Statement


Prove that a gun will shoot three times as high wehn its angle of elevation is 60deg as when it is 30deg but will carry the same horizontal distance.



Homework Equations


s=(Vo +Vf)/2 * t
x=Vo*costheta *t

The Attempt at a Solution



AFter simplifying the equation i get:

y=0.25tan30x
y=0.25tan60x

is this correct?
 
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The equations are right but you haven't shown that the range of the two angles are the same... or the height at 60 is 3 times the height at 30.

you've related the range to the height for each situation... but you haven't related range to range.. and height to height.
 

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