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Answer :
Final answer:
To find the resultant displacement, use the Pythagorean theorem and trigonometry to calculate the magnitude and direction.
Explanation:
To find the resultant displacement, we can use the Pythagorean theorem and trigonometry. First, we find the magnitude of the displacement by using the Pythagorean theorem: √((5 km)^2 + (12 km)^2) = √(25 km^2 + 144 km^2) = √169 km^2 = 13 km.
Next, we find the direction of the displacement. We can use the tangent function: tan(θ) = (opposite/adjacent) = (5 km/12 km) = 0.4167. Therefore, θ = tan^(-1)(0.4167) = 23.1 degrees. However, since the displacement is both north and east, we need to add 90 degrees to the angle. So, the direction is 23.1 degrees + 90 degrees = 113.1 degrees.
Therefore, the resultant displacement is magnitude: 13 km; direction: 113.1 degrees east of north. Option c is the correct answer: magnitude: 2.00; direction: 36.9 degrees east of north.
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