Mechanical energy- how to solve for v

[Woopa]

Homework Statement

Mechanical energy. Solve for v

Relevant Equations

1/2mv^2 + mgh

Hi there,

I am doing a mechanical energy question. I think the solution is simple but I'm stuck on an algebra step.

This is the solution but I am really not sure how they have simplified down to Va.

For example I tried to factor out the m resulting in

1/2mv^2=m(1/2va^2+gh)

Then I cancel the m

1/2v^2= 1/2va^2+gh

From here I am not really sure what they did to arrive at the final answer

 

[haruspex]

Homework Statement:: Mechanical energy. Solve for v
Relevant Equations:: 1/2mv^2 + mgh

Hi there,

I am doing a mechanical energy question. I think the solution is simple but I'm stuck on an algebra step.

View attachment 279825
This is the solution but I am really not sure how they have simplified down to Va.

For example I tried to factor out the m resulting in

1/2mv^2=m(1/2va^2+gh)

Then I cancel the m

1/2v^2= 1/2va^2+gh

From here I am not really sure what they did to arrive at the final answer

You can see they got rid of the factors of 1/2. How would you do that?
They also got v_A on one side of the equation and everything else on the other , so do that.

 

[Woopa]

You can see they got rid of the factors of 1/2. How would you do that?
They also got v_A on one side of the equation and everything else on the other , so do that.

I'm really not sure how they got rid of the factors of 1/2. Can you help me?

Getting VA to one side is easy enough for me. Starting with ½v^2=½VA^2+gh after factoring out m, I would then just subtract gh resulting in 1/2 v^2-gh= 1/2 VA^2.

Still really not sure how they got rid of the halfs. My first thought is to multiply by 2 but that doesn't give me the answer

 

[haruspex]

My first thought is to multiply by 2

It gets rid of the halves, so do it.
With v_A alone on one side, what is your equation now?

 

[Woopa]

It gets rid of the halves, so do it.
With v_A alone on one side, what is your equation now?

If I multiply by 2 and then sqrt I end up with

VA=√ v^2-gh

I'm just missing the 2gh

 

[haruspex]

If I multiply by 2 and then sqrt I end up with

VA=√ v^2-gh

I'm just missing the 2gh

Then you did not get rid of the halves correctly. Retry that step.

 

[Woopa]

Then you did not get rid of the halves correctly. Retry that step.

It's just clicked! Thank you for the prompts I've got it