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

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A stone is thrown downward from a height of 58.2 meters with an initial speed of 16.0 m/s, and the goal is to determine its final velocity at impact. The relevant equations include the kinematic equation and energy conservation principles. The calculated time of fall is approximately 3.88 seconds, leading to a final velocity of 54.1 m/s. There was confusion regarding the application of time in the equations, but it was clarified that rearranging the kinematic equation allows for solving the final velocity directly. The discussion emphasizes the importance of understanding both kinematic equations and energy conservation in solving projectile motion problems.
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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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