The resultant displacement is 12.2 km in a direction approximately 54.5 degrees east of north.
To find the resultant displacement, we can use vector addition since the man is traveling in two perpendicular directions. The distance traveled due north is 7.0 km, and the distance traveled east is 10.0 km. The resultant displacement is the vector sum of these two displacements.
Using the Pythagorean theorem, the magnitude of the resultant displacement (R) is given by
, which calculates to approximately 12.2 km.
The direction of the resultant displacement (θ) can be found using the tangent of the angle: tanθ= 7.0km/10.0km. Taking the arctangent of this ratio gives θ≈54.5∘.
Therefore, the resultant displacement is approximately 12.2 km in a direction of 54.5 degrees east of north. This represents both the magnitude and the direction of the man's overall displacement after traveling 7.0 km due north and 10.0 km east.