- #1

drnoisewater1

- 2

- 0

## Homework Statement

Two forces P and Q with respective magnitudes 100N and 200N are applied to the upper corner of a crate. The sum of the two forces is to the right (+x direction) with a magnitude of 250N. Find the angles that P and Q make with their sum - that is, with the horizontal line through +x axis.

## Homework Equations

R = P + Q where R is the resultant vector and P and Q are vectors given in the problem

Rx = Px + Qx = 250

Ry = Py + Qy = 0

## The Attempt at a Solution

All the information is given except the two angles. Plugging in the given values gives me the equation:

[tex]\Sigma[/tex]Rx = 100cos([tex]\theta[/tex]) + 200cos([tex]\phi[/tex]) = 250N

[tex]\Sigma[/tex]Ry = 100sin([tex]\theta[/tex]) - 200sin([tex]\phi[/tex]) = 0

where theta is the angle between P and R and phi is the angle between Q and R.

Basically this comes down to confusion on algebra for me. I attempted substitution and that got me nowhere. I know there is some kind of trick to solving this, but I cannot figure it out. There are two equations and two unknowns so there must be a way to do it. I have worked a similar problem where one of the angles is known and the other was supposed to be at a maximum and calculus could be used there. Is that a possibility in this problem or is there just a little trick that I am missing?