SOLUTION: A force f1, with magnitude 2n, and a second force f2, with magnitude 4n, act on a particle; they make an angle of 110 degrees with each other. Use trigonometric calculations to

Algebra ->  Trigonometry-basics -> SOLUTION: A force f1, with magnitude 2n, and a second force f2, with magnitude 4n, act on a particle; they make an angle of 110 degrees with each other. Use trigonometric calculations to       Log On


   



Question 366802: A force f1, with magnitude 2n, and a second force f2, with magnitude 4n, act on a particle; they make an angle of 110 degrees with each other.
Use trigonometric calculations to find the magnitude of the resultant force and the angle it makes to the force .

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let the direction of force f1 be the x direction.
f1=(2n,0)
Force f2 can be then broken down into x and y components.
f2=(4n%2Acos%28110%29,4n%2Asin%28110%29)
f2=(-1.37n,3.76n)
The resultant force f is then,
f=f1%2Bf2
f=(2n,0)+(-1.37n,3.76n)
f=(2n-1.37n,3.76n)
f=(0.63n,3.76n)
The tangent of the angle is
tan%28theta%29=3.76%2F0.63
tan%28theta%29=5.97
theta=80.5degrees
The angle theta is measured with respect to f1.