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

[Reth0407]

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

 

[rude man]

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.

 

[Reth0407]

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

 

[gneill]

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 (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.

 

[Reth0407]

Ok I got it! LIke gneill said, I could rearrange the equation and solve for vx. Thank you all.