Speed of objects as they hit the ground

  • Context: Undergrad 
  • Thread starter Thread starter yrjosmiel
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Discussion Overview

The discussion revolves around the comparison of the speeds of two objects as they hit the ground: one thrown directly downward and the other thrown horizontally, both from the same height. The focus includes the application of kinematic equations and energy conservation principles.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents calculations for the final speed of both objects, suggesting that the final speed for the object thrown downward is given by the equation vfy = sqrt(v0^2 + 2ah).
  • Another participant proposes using energy conservation as an alternative method to analyze the problem.
  • Some participants agree that the speeds will match when considering conservation of energy, while noting that the velocities of the two objects will differ.
  • There is a suggestion that the speeds of the two objects will be the same upon impact, but this is contested by another participant who clarifies that while the speeds may match, the velocities will not.

Areas of Agreement / Disagreement

Participants generally agree that the speeds of the two objects will be the same at impact, but there is disagreement regarding the distinction between speed and velocity, as well as the implications of energy conservation.

Contextual Notes

The discussion does not resolve the potential assumptions regarding the effects of air resistance or other external factors that could influence the results.

yrjosmiel
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Let's say there are two objects. One is thrown directly downward at v0 and the other is thrown horizontally (90 degrees) at v0, both from height h. Which object will have a higher speed by the time they hit the ground? Would they have the same speed?

For the object thrown downward...
h = (vf2 - v02)/2a
vfy axis = sqrt(v02 + 2ah)
final speed = sqrt(v02 + 2ah)

For the object thrown horizontally
vy axis = sqrt(2ah)
vx axis = v0
add the two vectors
vftotal = sqrt(v02 + 2ah)

Is this right? Or have I miscalculated something in the way?
 
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You can also use energy conservation here.
 
Looks good to me. The matching velocities speeds make sense when you consider conservation of energy.
 
Last edited by a moderator:
The velocities won't be the same but the speeds will.
 

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