Another trans formula, bit harder!

[yohanson77]

Hello,
Got another trans formula, this had me puzzled for hours:

Q. The total energy within a dynamic system is given by:

E = mgh + 1/2mv^2 + L

Make 'v' the subject, and hense determine the velocity when:

m=750 kg, g=9.81 m/s^2, h=1 x 10^3 meters, L=3x10^4 J, and E=56 x 10^6 J.

I'm ok at adding in the figures, it's mainly the transposition.

Thank you for your time.

Yohanson

 

[jonboy]

M

Unless there's some physic rule that I'm unaware of, this is not too difficult.

I'll assume you mean this:\(\displaystyle \L \;E =\,mgh\,+\,\frac{1}{2}mv^2\,+\,L\)

Subtract \(\displaystyle mgh\) and \(\displaystyle L\) from both sides: \(\displaystyle \L \;E\,-\,mgh\,-\,L\,=\,\frac{1}{2}mv^2\)

Multiply both sides of the equation by 2 and \(\displaystyle \frac{1}{m}\): \(\displaystyle \L \;\frac{2E\,-\,2mgh\,-\,2L}{m}\,=\,v^2\)

Take the square root of both sides: \(\displaystyle \L \;v\,=\,\sqrt{\frac{2E\,-\,2mgh\,-\,2L}{m}}\)

...I might be wrong but I'm feeling pretty confident.

Now you have v as the subject, can you complete the problem?

 

[morson]

jon did well, but velocity can be both positive and negative. So the negative of that square root applies as well.