What is the final velocity of a stone thrown downwards from a roof?

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Homework Help Overview

The discussion revolves around a physics problem involving the motion of a stone thrown vertically downward from a height of 58.2 meters with an initial speed of 16.0 m/s. Participants are exploring how to determine the final velocity of the stone upon impact with the ground.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss using energy conservation principles and kinematic equations to find the final velocity. Some express confusion about the correct application of equations and the calculation of time. Others question the values obtained for time and final velocity, indicating uncertainty in their calculations.

Discussion Status

The discussion is active, with participants sharing different approaches and expressing confusion about specific calculations. Some guidance has been offered regarding rearranging equations to solve for final velocity, but there is no explicit consensus on the correct values or methods.

Contextual Notes

Participants mention constraints such as the instructor's equations involving variables for velocity and position, which adds to the complexity of the problem. There is also uncertainty about the appropriateness of the calculated time value.

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Homework Statement


A person throws a stone vertically downward with an initial speed of 16.0m/s from the roof of a building 58.2m above the ground.
What velocity does the stone have at impact?


Homework Equations



initial x= 58.2m initial vox=16.0m/s ax= 9.81m/s^2 xfinal=0 vx=?

2a(x-xo)=vx^2-vox^2 to find t= 3.88

vx=vox+axt plug in a number including t=3.88 vx= 54.1



The Attempt at a Solution


2 attempts with only 2 attempts left. Please help
 
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Simplest way is use nergy conservation: initial kinetic energy + loss of potential energy = final kinetic energy.

Other way: v = v0+ gt
h = ∫v(t)dt = v0t + gt2/2 & solve for t = time of fall
h = height of building
Then stick t into the v equation above.
 
I am still confused on how I would plug the numbers because the instructor have me equations with v and x variables. However, are my numbers correct for time=3.88 s and my vx = 54.1 m/s which I'm sure isn't correct. I'm solving for vx
 
Reth0407 said:

Homework Statement


A person throws a stone vertically downward with an initial speed of 16.0m/s from the roof of a building 58.2m above the ground.
What velocity does the stone have at impact?


Homework Equations



initial x= 58.2m initial vox=16.0m/s ax= 9.81m/s^2 xfinal=0 vx=?

2a(x-xo)=vx^2-vox^2 to find t= 3.88
t doesn't appear in the equation, so how do you obtain t from it :confused: (Also, that doesn't look like a correct value for t for this situation).

However, you can use that equation to find the final velocity, vx. Rearrange the equation to solve for vx.
 
Ok I got it! LIke gneill said, I could rearrange the equation and solve for vx. Thank you all.
 

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