Concept:The range of possible values for the resultant of two vectors.
Formula:$$|F_1 - F_2| \le R \le F_1 + F_2$$
Solution:Given \(F_1 = 50\text{ N}\) and \(F_2 = 20\text{ N}\):
- The minimum possible resultant magnitude occurs when the two forces act in opposite directions (\(\theta = 180^\circ\)):
$$\text{Min Resultant} = 50\text{ N} - 20\text{ N} = 30\text{ N}$$ - The maximum possible resultant magnitude occurs when they act in the same direction (\(\theta = 0^\circ\)):
$$\text{Max Resultant} = 50\text{ N} + 20\text{ N} = 70\text{ N}$$
The magnitude of the resultant force must fall within the range \([30\text{ N}, 70\text{ N}]\). Since 20 N is less than 30 N, it cannot be a possible resultant force.
Why other options are incorrect:- 30 N is the minimum limit (opposite direction).
- 40 N is within the valid range.
- 70 N is the maximum limit (same direction).
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