Where Does the Square Root of gd/2 Come From?

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Homework Help Overview

The discussion revolves around the origin of the expression sqrt(gd/2) in the context of projectile motion, particularly relating to velocities and heights in a physics problem. Participants are exploring the relationship between initial velocity components and gravitational effects on a projectile.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the derivation of the expression sqrt(gd/2) and its significance in relation to initial velocity and height. Questions are raised about the meaning of the components of the equation and the conditions under which the velocities are equal.

Discussion Status

The discussion is ongoing, with participants expressing confusion about the derivation and meaning of the expression. Some guidance has been offered regarding the relationship between the velocities, but there is no consensus on the origin of the sqrt(gd/2) term.

Contextual Notes

There is mention of a specific equation, vf² = vi² + 2ad, and uncertainty about the factors involved, particularly the 1/2 in the context of gravitational acceleration and distance. Participants are also reflecting on their previous contributions and seeking clarification.

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Homework Statement


See picture please

Homework Equations


The Attempt at a Solution


Here is what I understand:
vi sin(theta) = initial velocity height on velocity/time graph
What I don't understand:
sqrt(gd/2) is this gravity times initial distance height of target?
Where is the second side of the equation is coming from?
 

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[tex]\sqrt{\frac{gd}{2}}[/tex]= some velocity that is less than or equal to vsintheta which is another velocity. So when d is at the maximum height both sides should equal each other
 
ok, i understand that it is a velocity, but where is it coming from? why is is the square root of gd/2?
 
i re read your problem and I'm sorry i gave the wrong advice.

umm vf2 = vi2+2ad

not sure where the 1/2 came from. sorry its late
 
So from the equation that you posted, they are deriving vi sintheta is greater than or equal to sqart (gd/2)?
 
ok, i understand that it is a velocity, but where is the square root of gd/2 coming from? anyone?
 

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