Discover the Meaning of Δy in Projectile Motion Formula: A Comprehensive Guide

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Discussion Overview

The discussion revolves around the interpretation of the formula Δy=[(sin2θ)(Vi)]^2/2a in the context of projectile motion. Participants explore what this formula signifies, particularly regarding the height it represents in projectile motion scenarios.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on what Δy represents in the formula, specifically asking about the height indicated by the equation.
  • Another participant suggests that the formula is similar to the one for the distance a projectile travels, questioning whether there was a misreading of the formula.
  • A participant proposes that Δy could represent the maximum height over flat ground, indicating a possible understanding of the formula's application.
  • Another participant confirms that the formula indeed represents the maximum height, based on their research.
  • A later post corrects the original formula by suggesting that sin2θ should be replaced with sinθ for it to accurately represent the maximum height of a projectile.
  • One participant provides a derivation of the maximum height formula using the kinematic equation, indicating the vertical component of velocity and how it relates to the maximum height attained by a projectile.

Areas of Agreement / Disagreement

There is no clear consensus on the interpretation of the formula Δy, as participants present differing views on its correct form and meaning. Some agree that it relates to maximum height, while others suggest corrections to the formula itself.

Contextual Notes

Participants express uncertainty regarding the correct form of the formula and its implications, with some acknowledging the need for clarification on the angle representation and the variables involved.

Who May Find This Useful

This discussion may be useful for students or individuals interested in understanding projectile motion, particularly those seeking clarification on the mathematical representations and interpretations of related formulas.

staka
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I would like to simply know what Δy=[(sin2θ)(Vi)]^2/2a represents..
The formula only requires the angle and the initial velocity (along with the usual a=9.8m/s^2), so what height does the equation represent?
 
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The distance a projectile travels (over flat ground) is [sin(2θ)*(v^2)]/a, very similar to what you have there. Is there a chace you misread it?
 
well that's the distance..
I think I got it now though, it's possibly the maximum height over a flat ground.
 
Oh yeah you're correct, i just googled it a bit and it came up. It is the maximum height you reach
 
staka said:
I would like to simply know what Δy=[(sin2θ)(Vi)]^2/2a represents..
The formula only requires the angle and the initial velocity (along with the usual a=9.8m/s^2), so what height does the equation represent?
That's almost the formula for the maximum height of a trajectory. To correct it, replace sin2θ with sinθ.
 
So one of the famous equations for the motion of a projectile is as follows:

v2=u2+2as

v = final velocity
u = initial velocity
a = g = -9.8m/s2
s = distance travelled

Now, for a projectile being fired at an angle, the vertical component of velocity is usin%, where % is the angle between the ground and the direction of projection.

Rearrange your equation, with v=0 to get the maximum height attained by a projectile (note that in your equation, your v is my u).

You get:

s = u2/-2a = (usin%)2/-2a

As a = -9.8, you can ignore the minus sign and you basically have your equation (except for the sin2% bit).

Yes I don't know how to make greek alphabet symbols, so a % for an angle will do :D

Hope that helps.
 

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