Solve Fraction Problem: F2 = [ (v + v2)/(v + v1) ] F1

[sapiental]

Hey,

I'm terrible with fractions and would appreciate any help regarding this problem.

This is a problem from my physics course.

F2 = [ (v + v2)/(v + v1) ] F1

I need to solve for v1. I am given the values for F2, v, v2, and F1 and need to turn the formula around to solve for v1..

F1 = 400
F2 = 420
v = 344
v2 = 26.82

My attempt was F2/(F1(v+v2)) = 1 / (v+v1)

but this is wrong..

any suggestions?

 

[courtrigrad]

$$F_{2} = \left \frac{v+v_{2}}{v+v_{1}}\right F_{1}$$So $$F_{2}(v+v_{1}) = F_{1}(v+v_{2})$$

$$v + v_{1} = \frac{F_{1}(v+v_{2})}{F_{2}}$$

$$v_{1} = \frac{F_{1}(v+v_{2})}{F_{2}} - v$$

 

[Architeuthis Dux]

Sure, here is how to solve this problem:

First, let's simplify the fraction on the right side by multiplying both the numerator and denominator by (v+v1):

F2 = [ (v + v2)/(v + v1) ] F1

F2 = (v + v2) F1 / (v + v1)

Next, we can distribute the F1 to both terms in the numerator:

F2 = vF1 + v2F1 / (v + v1)

Now, we can rearrange the equation to isolate v1 on one side:

F2(v + v1) = vF1 + v2F1

F2v + F2v1 = vF1 + v2F1

F2v1 - vF1 = vF1 - vF1 + v2F1

F2v1 - vF1 = v2F1

Finally, we can divide both sides by F2 and then multiply by -1 to isolate v1:

-1(F2v1 - vF1) = -1(v2F1)

-v1 = -v2F1/F2

v1 = v2F1/F2

Therefore, the solution for v1 is:

v1 = (v2F1)/F2

Substituting in the given values, we get:

v1 = (26.82 * 400)/420

v1 = 25.54

So, v1 is approximately 25.54. I hope this helps! Remember to always check your work and plug the value of v1 back into the original equation to make sure it satisfies the problem. Good luck!