Projectile without air resistance

AI Thread Summary
In a discussion about projectile motion without air resistance, participants explore the relationship between the maximum range and maximum height of a projectile. The key equation presented is R = 4hmax, which relates the range to the maximum height. Questions arise regarding the derivation of the factor of 4 and the implications of optimizing the launch angle for maximum range. Participants express confusion over how to calculate the projectile's speed at the optimal angle and the role of time in the equations. The conversation emphasizes the need for clarity in the equations governing projectile motion to solve the problem effectively.
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Homework Statement



Consider a projectile without air resistance. Show
that when the range is maximized, it may be given
in terms of the maximum height

Homework Equations


R = 4hmax


The Attempt at a Solution


I tried looking upon the equation for the vector R but could not understand where 4h came from. Is the max pertaining to velocity =0 ?
 
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Write out the equation for range. What's the projectile's speed of launch if its launch angle is optimized? Using this speed and the optimal angle, can you calculate maximum height?
 
I appreciate the help for this problem :]
 
To find out the projectile speed given that the launch angle is optimized is giving me a hassle because the equation for y or x has time in it. Or am i using the wrong equation?
 
Yes,the formula for max height does not have x,y or t.
 

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