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Two forces have magnitudes whose sum is 18 N. Their resultant has magnitude 12 N and is at right angles to the smaller force. What are the magnitudes of the two forces?

1. 12 N and 6 N
2. 13 N and 5 N
3. 10 N and 8 N
4. 16 N and 2 N

Correct answer: 13 N and 5 N

Solution

The two forces must satisfy both the condition of their magnitudes summing to 18 N and the Pythagorean theorem, as the resultant is at right angles to the smaller force. The only pair that meets these criteria is 13 N and 5 N, where 13 N is the larger force and 5 N is the smaller force, resulting in a correct resultant of 12 N.

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