Final answer:
The man's total displacement for the trip is approximately 58.62 meters at an angle of 25.57° north of east.
Step-by-step explanation:
To find the man's total displacement for the trip, we can use the graphical technique for adding vectors. We need to find the eastward and northward displacements and then combine them to find the resultant displacement.
The man drives 53 meters to the east, which gives us an eastward displacement of 53 meters. Then, he turns and drives 25 meters to the north, which gives us a northward displacement of 25 meters.
To find the resultant displacement, we can use the Pythagorean theorem. The magnitude of the resultant displacement is the square root of the sum of the squares of the eastward and northward displacements:
Resultant displacement = sqrt((53^2) + (25^2)) = sqrt(2809 + 625) = sqrt(3434) ≈ 58.62 meters.
The direction of the resultant displacement can be found using trigonometry. The tangent of the angle can be calculated as the ratio of the northward displacement to the eastward displacement:
Tan(angle) = 25/53 = 0.4717
Angle = arctan(0.4717) ≈ 25.57° north of east.