Question

Two forces whose resultant is 100 N are at an angle to each other. If one of them makes an angle of 30° with the resultant, determine its magnitude.

a) 50 N
b) 70 N
c) 80 N
d) 90 N

Answer 1

To find the magnitude of the force that makes an angle of 30° with the resultant of two forces, we can use the law of cosines. By setting up and solving a quadratic equation, we find that the magnitude of the force is approximately 89.44 N.

Step-by-step explanation:

To determine the magnitude of the force that makes an angle of 30° with the resultant of two forces, we can use the law of cosines. Let's call the magnitude of the unknown force F1. We can set up the equation as F1^2 = 100^2 + X^2 - 2(100)(X)cos(30°), where X is the magnitude of the other force. Simplifying this equation gives us F1^2 = 10000 + X^2 - 200Xcos(30°). Since we know that F1^2 = 200X^2, we can substitute this into the equation to get 200X^2 - 10000 + X^2 - 200Xcos(30°) = 0. Solving this quadratic equation gives us X ≈ 89.44 N.