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Answer :
Final answer:
To determine the resultant force, you can decompose the given forces into their x and y components and then add the components separately. The magnitude of the resultant force can be found using the Pythagorean theorem, and the direction can be found using trigonometry.
Explanation:
In order to determine the resultant force, we will use the concept of vector addition. We can decompose the given forces into their x and y components. The first force of 62 N at 30 degrees can be written as 62*cos(30)i + 62*sin(30)j, and the second force of 62 N at 60 degrees can be written as 62*cos(60)i + 62*sin(60)j. Adding the x and y components separately, we get 62*cos(30) + 62*cos(60) and 62*sin(30) + 62*sin(60), respectively. By calculating these values, we find that the resultant force is approximately 0.866i + 89.9j N.
To find the magnitude of the resultant force, we can use the Pythagorean theorem: |R| = sqrt((0.866)^2 + (89.9)^2) ≈ 89.9 N.
The direction of the resultant force can be found using trigonometry: tan(theta) = (62*sin(30) + 62*sin(60)) / (62*cos(30) + 62*cos(60)). By calculating this expression, we find that theta ≈ 89 degrees.
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