Maximum height of a projectile

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The discussion focuses on deriving the relationship between the maximum height (H) of a projectile and its range (R), specifically proving that H/R = 1/4 tan(theta). Participants suggest starting by analyzing the projectile's behavior at maximum height and calculating its height and range using kinematic equations. The calculations should involve the initial speed (v) and launch angle (theta). By establishing the mathematical relationships for both height and range, the ratio can be determined. The conversation emphasizes a systematic approach to solving the problem through kinematics.
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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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