Calculating Final Velocity of Free Falling Objects

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Discussion Overview

The discussion revolves around the calculation of the final velocity of free-falling objects, particularly in the context of sign conventions and the application of kinematic equations. Participants explore the implications of defining directions as positive or negative and how this affects the interpretation of velocity in free fall scenarios.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Homework-related

Main Points Raised

  • Some participants note that sign conventions for velocity are arbitrary and depend on whether "up" or "down" is defined as positive.
  • One participant questions the meaning of 'final' velocity, suggesting that an object in free fall can be moving in different directions depending on the problem context.
  • A participant presents a specific problem involving a cliff diver and discusses the expected final velocity using the kinematic equation, leading to confusion over the sign of the answer.
  • Another participant asserts that if down is defined as negative, then the final velocity of the diver should indeed be negative, supporting the site's answer of -44.6 m/s.
  • Concerns are raised about potential errors in calculations, particularly regarding the use of square roots and the necessity of applying the correct sign based on the direction of motion.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of final velocity and the application of sign conventions. There is no consensus on the resolution of the confusion regarding the calculations, as some participants affirm the site's answer while others express uncertainty about their own calculations.

Contextual Notes

Limitations include the dependence on the chosen sign convention and the potential for misunderstanding the application of kinematic equations in different contexts. The discussion does not resolve the discrepancies in calculations or interpretations.

tawnyman
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just a quick question! will the final velocity of a free falling object always be negative even if the answer is positive?
 
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tawnyman said:
just a quick question! will the final velocity of a free falling object always be negative even if the answer is positive?

Hi, welcome to PF!

Sign conventions are arbitrary. It's up to you whether you define "up" to be the positive direction, or "down" to be the positive direction.

That having been said, if you have defined "down" to be negative, and you know that an object is supposed to be moving downward, yet you get a positive answer for its velocity, then your answer is incorrect given the sign convention you chose.
 
tawnyman said:
just a quick question! will the final velocity of a free falling object always be negative even if the answer is positive?
:confused:

Not sure what you mean by 'final' velocity, but something in freefall can be moving up or down depending upon the exact problem. (Or not moving at all, for an instant.)
 
thanks so much! that's what i thought, but then there's this question i was trying out (don't worry, it's not homework. found it online so i could practice):

A cliff diver from the top of a 100 [m] cliff. He begins his dive by jumping up
with a velocity of 5 [m/s]. What is his velocity right before he hits the water?

if down is defined as negative and the equation used is vf^2=vi^2+2ad then the answer should be 44.6m/s but the answer on the site was -44.6m/s.
 
tawnyman said:
if down is defined as negative and the equation used is vf^2=vi^2+2ad then the answer should be 44.6m/s but the answer on the site was -44.6m/s.
He's moving down so his velocity should be negative. The site's answer is correct.
 
i MUST be doing something wrong.@_@ or I'm inputting something wrong in my calculator. so the square root of 5^2 + 2(-9.8)(-100) is positive?
 
tawnyman said:
i MUST be doing something wrong.@_@ or I'm inputting something wrong in my calculator. so the square root of 5^2 + 2(-9.8)(-100) is positive?
The calculator only gives you the positive square root of a number. You have to supply the negative sign based on your understanding of how he's moving. (Don't forget that a negative number squared is positive.)
 
Doc Al said:
You have to supply the negative sign based on your understanding of how he's moving. (Don't forget that a negative number squared is positive.)

that's totally the answer to my first question.=D thanks!
 

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