Solving First-Year Physics Textbook Puzzle: Adding Squared Equations

[mohdhm]

ok this is in an example in a first-year physics textbook, yet some how i spent an hour trying to solve it (identities, tricks, etc) and could not find a solution.

here is what the textbook states:
(1) v2f*cos\phi = 3.5*10^5 - v1f*cos(37)
(2) v2f*cos\phi = v1f*sin(37)

"now we sqaure these two equations and add them"

= 1.23*10^11 - 7*10^5*v1f*cos(37) + v1f^2*cos(37)^2 + v1f^2*sin(37)^2

(then it simplifies further)

I know that 1.23*10^11 is (3.5*10^5)^2 and that 7*10^5 is 2*3.5*10^5any help in explaining how this equation is derived would be a great help (ESPECIALLY how 7*10^5 seems to pop out of no where)

 

[neutrino]

Did you try squaring and adding the terms?

 

[Extropy]

any help in explaining how this equation is derived would be a great help (ESPECIALLY how 7*10^5 seems to pop out of no where)

More importantly, where did that cos(37) come from?

 

[mohdhm]

sorry the cos 35 is supposed to be cos 37. my mistake.

Yes i did try adding them and squaring them. your point? why the **** would i take the time to ****ing type it down clearly for your convenience.

 

[neutrino]

Yes i did try adding them and squaring them. your point?

You obviously missed something doing that. Remeber that -2ab when expanding (a-b)^2?

 

[mohdhm]

lol, you know what... i didn't forget that i should get -2ab... i made an even dumber mistake... i did (a^2 - b^2)

wow... thanks for pointing it out though, holy crap.