Forces A and B have magnitudes of 10.0 N and 20.0 N, respectively. What is the magnitude of their sum when A is directed along \theta=0^\circθ = 0 ∘ and B is directed along \theta=50^\circθ = 50 ∘?

The magnitude of the sum of A and B is 27.51 N.

Explanation:

We can separate the x- and y-components of the vectors, then sum these components separately. Afterwards, we can calculate the magnitude of the sum.

On the other hand, for the vector B:

The sum of the components in the x-direction is equal to 22.85 N.

The sum of the components in the y-direction is equal to 15.32 N.

Finally, the magnitude of the sum vector C is

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