Two forces of equal magnitude act to 60 degrees. If their resultant has a magnitude of 30N, find the magnitude of the equal forces.

To find the magnitude of the equal forces, we can use the concept of vector addition. The resultant of two forces can be found using the law of cosines.

Let's call the magnitude of the equal forces as "F". According to the given information, the resultant has a magnitude of 30N and the angle between the two forces is 60 degrees.

Using the law of cosines, we can write:

Resultant^2 = Force1^2 + Force2^2 - 2 * Force1 * Force2 * cos(angle)

Substituting the given values:

30^2 = F^2 + F^2 - 2 * F * F * cos(60)

Simplifying this equation:

900 = 2F^2 - 2F^2 * cos(60)

900 = 2F^2 - F^2

900 = F^2

Taking the square root of both sides:

F = √900

F = 30

Therefore, the magnitude of the equal forces is 30N.

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