Answer :
Final answer:
The resultant of an easterly force of 218 N and a southerly force of 157 N can be found using the Pythagorean theorem. This formula calculates the magnitude of the resultant force and the direction can be calculated using the arctan of the ratio of the two forces.
Explanation:
In physics, we often have to calculate the resultant of two forces acting at an angle. The relevant concept here is vector addition. When two forces, say an easterly force of 218 N and a southerly force of 157 N, are acting upon an object, the resultant force is given by the Pythagorean theorem, as we are effectively dealing with two sides of a right-angled triangle (where the forces are the two sides, and the resultant is the hypotenuse).
To calculate the magnitude of the resultant force, we can use this formula:
Resultant Force = √((Easterly Force)² + (Southerly Force)²)
So, substituting the given values into this equation:
Resultant Force = √((218 N)² + (157 N)²)
By doing this calculation, we find the resultant force. Its direction would be given by the angle whose tangent is the ratio of the Southerly Force to the Easterly Force, or in other words, the arctan (Southerly Force/Easterly Force). This angle would be measured from the east (as we typically measure angles counterclockwise from the positive x-axis, which is to the east).
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