Solving for Velocity Vector Angle of 45.0

[blufoggy]

Homework Statement

If http://net.dinhweb.de/vector.gif ,[/URL] where b and c are positive constants, when does the velocity vector make an angle of 45.0 with the x- and y-axes?

Homework Equations

I'm not sure.. I've got a million equations but none of them seem to fit the problem the way I need. I know this isn't relevant to the question, but the prompt asks for "t=?"

The Attempt at a Solution

I've got this thing worked down to b divided by c (b/c), but apparently my "answer is off by a multiplicative factor." I've already taken a few shots at guessing the coefficient I need, but no luck there, so I decided to give this a try.

I didn't think any kind of "multiplicative factor" was necessary because equal "i hat" and "j hat" values would give a 45 degree angle. Apparently not and here I am stuck on this problem

Any kind of help would be greatly appreciated =]

 

[cristo]

Do you know how to use the scalar product to determine the angle between two vectors? i.e.\bold{x}\cdot \bold{y}=xy\cos\theta where \theta is the angle between the two vectors.

 

[blufoggy]

Somewhat.. Researching the answer earlier through my textbook actually led me to the exact page with the scalar product definition, but I couldn't figure out how it tied into the problem.

It's actually a couple chapters back from the original problem, but now I'm in the process of reading it over again.

 

[cristo]

Well, try looking at r.i and r.j, since you know the angle that r must make with the x and y axes.

 

[blufoggy]

Hm.. I think I understand a little better now..

So I have the component direction and magnitude, but finding the dot product of r and i or r and j gives me the magnitude of r which is the component of either i or j? And that magnitude is the factor I'm missing?

 

[civil_dude]

I have looked at this, and plugged b/c into excel and it works for 5 different b and c constants. Thus for me, b/c is correct.

 

[blufoggy]

Well I feel stupid..

Someone hinted to "find the derivative of the positive vector".. Which meant next to nothing to me, but I decided to give it a try anyway and use the coefficients I would've gotten if I took the derivative of the whole equation. It turns out the "mutiplicative factors" I was missing was a 2 and 3, so the answer was..

t = (2b)/(3c)

I don't know if it's just me, but that answer doesn't make any sense and now I'm more confused than ever.