Question #e4d6c

1 Answer
Sep 4, 2017

theta = 120^"o"

Explanation:

We're asked to find the necessary angle between two force vectors so that the resultant vector has a magnitude equal to that of one of the forces.

Let's make the two force vectors have magnitudes A and B, and their resultant have magnitude C. We can use the law of cosines:

C^2 = A^2 + B^2 - 2ABcostheta

Since the two vector magnitudes A and B are equal, we can just replace B with A:

C^2 = 2A^2 - 2A^2costheta

Now, let's find the angle theta between the constituent forces:

costheta = (2A^2 - C^2)/(2A^2)

And since the resultant force's magnitude is equal to that of one of the vector magnitudes, C = A:

costheta = (2A^2 - A^2)/(2A^2)

costheta = 1/2

color(red)(ulbar(|stackrel(" ")(" "theta = 120^"o"" ")|)

The angle between the two force vectors must be color(red)(120^"o".