Maximum height of a projectile

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Homework Help Overview

The discussion revolves around the relationship between the maximum height of a projectile and its range, specifically exploring the ratio H/R and its connection to the tangent of the launch angle.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants suggest starting with the properties of a projectile at maximum height and deriving mathematical relationships for both height and range. There are inquiries about the behavior of a projectile at its peak height and the necessary kinematic equations to describe its motion.

Discussion Status

The conversation is active, with participants offering guidance on how to approach the problem by breaking it down into components related to kinematics. Multiple lines of reasoning are being explored without a clear consensus on the next steps.

Contextual Notes

Participants are working within the constraints of deriving relationships based on kinematic equations, with an emphasis on understanding the underlying physics rather than jumping to conclusions.

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Prove that the maximum height of a projectile H, divided by the range of the projectile, R, satisfies the relation H/R = 1/4 tan.


I have no idea how to do this
 
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Why don't you start by figuring out what happens to a projectile at its max heights and then find a mathematical relationship for that. Then do the same for the range, and see what you can come up with.
 
what happens to a projectile at its max heights ?
 
Calculate the height in terms of v which is the speed, and theta which is the angle.

Calculate the range in terms of v and theta.

Take the ratio, and the result follows.

To get the range and height... begin by writing the 2 kinematics equations (that give horizontal and vertical displacement for any time)
 

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