Question

Question #e4d6c

Answer 1

`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"`.