Projectile without air resistance

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Homework Help Overview

The discussion revolves around a projectile motion problem, specifically analyzing the relationship between the range and maximum height of a projectile in the absence of air resistance.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the equation for range and its connection to maximum height, questioning the origin of the factor of 4 in the relationship. There are attempts to derive the projectile's speed at an optimized launch angle and its implications for calculating maximum height.

Discussion Status

The discussion is ongoing, with participants providing insights and asking clarifying questions. Some have expressed difficulty in relating the equations of motion to the problem, particularly regarding the role of time in the equations for range and height.

Contextual Notes

Participants are navigating constraints related to the equations of motion and the specific conditions of the problem, such as the absence of air resistance and the optimization of launch angle.

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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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