Projection angle using max. height w/ proportions only

AI Thread Summary
The discussion revolves around a projectile motion problem where the speed at maximum height is half the speed at half maximum height. The key equation provided is h = (vi^2 sin^2 theta)/2g, which relates height to initial velocity and angle. The original poster struggles to begin the problem, contemplating the division of height and questioning their understanding of velocity components. Suggestions include breaking down velocity into its x and y components at half maximum height to find the speed. The conversation emphasizes the importance of understanding the relationship between speed and height in projectile motion.
amphiprion86
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Figures that the only problem I have trouble with is the one the book considers to be "easy":

Homework Statement


The speed of a projectile when it reaches its maximum height is one half its speed when it is at half its maximum height. What is the initial projection angle of the projectile?


Homework Equations


h= (vi^2 sin^2 theta)/2g


The Attempt at a Solution



Complete brain fart--I don't even know where to start, beyond trying to divide h/2, which would be (vi^2 sin^2 theta)/4g, correct? That's about as far as I got. I just keep miring myself the further into it I go.
 
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Speed of course is the magnitude of velocity. At its maximum height a projectile only has one component of velocity. Is that enough to get you started?
 
Try breaking velocity into x and y components @ 1/2 max height and then finding speed from there the "sqrt of the sum of the squares".
 

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