Transposing formulas

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davehogan

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I have to re-arrange "E=1/2mv2+mgh" to make the subject "m". The answer given is "m=2E/v2+2gh". I can't get to this answer. My workings are:

E=1/2mv2+mgh.

2E=mv2+2mgh. Multiply both sides by 2.

2E/v2=m+2mgh. Divide both sides by v2.

2E/v2+gh=2m. Divide both sides by gh.

That's the best I can do. Can anyone explain this for me, please?
 
davehogan said:
I have to re-arrange "E=1/2mv2+mgh"...
Click to expand...
As posted, the above (arguably) means the below:

. . . . .\(\displaystyle E\, =\, \dfrac{1}{2mv^2}\, +\, mgh\)

Was this what you meant? If not, kindly please reply using grouping symbols to make clear what all is in the denominator. Thank you! ;)
 
Many thanks. I've got it OK now. I won't bother my teacher, I'll go straight to a neurosurgeon to see if there's any kind of intelligence between my ears.
 
stapel said:
As posted, the above (arguably) means the below:

. . . . .\(\displaystyle E\, =\, \dfrac{1}{2mv^2}\, +\, mgh\)

Was this what you meant? If not, kindly please reply using grouping symbols to make clear what all is in the denominator. Thank you! ;)
Click to expand...
Isn't this 1/2/m/v^2+mgh

I believe the OP is correct.
 
davehogan said:
I have to re-arrange "E=1/2mv2+mgh" to make the subject "m". The answer given is "m=2E/v2+2gh". I can't get to this answer. My workings are:

E=1/2mv2+mgh.

2E=mv2+2mgh. Multiply both sides by 2.

2E/v2=m+2mgh. Divide both sides by v2.

2E/v2+gh=2m. Divide both sides by gh.

That's the best I can do. Can anyone explain this for me, please?
Click to expand...

I am posting this just because it feels great to tell someone about what I know and able to help someone even though it is a late response

You are not suppose to divide v2 both sides.
since m is suppose to be the subject,both mv2 and mgh have the variable m.
so it should have been 2E=m(v2+2gh)
then divide v2+2gh from both sides.
and you get the answer m=2E/v2+2gh
 
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Prof.Hakugen said:
I am posting this just because it feels great to tell someone about what I know and able to help someone even though it is a late response

You are not suppose to divide v2 both sides.
since m is suppose to be the subject,both mv2 and mgh have the variable m.
so it should have been 2E=m(v2+2gh)
then divide v2+2gh from both sides.
and you get the answer m=2E/v2+2gh
Click to expand...
The response above is incorrect. As written, it expresses:

\(\displaystyle m = \frac{2E}{v^2} \ + \ 2gh\).....................which is wrong.

The correct intended answer is:

\(\displaystyle m = \frac{2E}{v^2 \ + \ 2gh}\)

which should be written as:

m=2E/(v2+2gh)

Those parentheses () are super important to convey the correct answer following PEMDAS.
 
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