Phyics Force question?

Question

A force F = Fxi + Fyj acts on a object with Fx = 5 N and Fy= 6N
The angle between F and the displacement vector s is 36 and 130 J of work is done by F.

What is the magnitude of vector s

Answer 1

This question is tricky because you need to first solve for F and then drop all of the Fx and Fys because the displacement vector is indepedent of the Fx and Fys. (Keeping them in the equation will lead to multiple solutions and confusion).

First find F using the pythagorean thereom.

F^2= Fx^2 +Fy^2
F=squr(25+36)

Now for Work
W=F*d

Remember that d is displacement in the direction of the Force, therefore
d=s*cos(theta)

Substituting s for d

s=W/(F*cos(theta))

I'll let you plug in the numbers.