Final answer:
To find the resultant displacement, establish a coordinate system and add the displacements vectorially. The magnitude is approximately 42.4 m and the direction is 135° east of north.
Step-by-step explanation:
To find the magnitude and direction of the resultant displacement algebraically, we need to establish a coordinate system. Let's consider the north direction as positive y-axis and east direction as positive x-axis.
First, we walk 30 m south, which means a displacement of -30 m along the y-axis. Then, we walk 30 m east, which means a displacement of +30 m along the x-axis.
To find the resultant displacement, we can add these two displacements vectorially. The magnitude of the resultant displacement can be found using the Pythagorean theorem: magnitude = sqrt((-30)^2 + 30^2) = sqrt(900 + 900) = sqrt(1800) ≈ 42.4 m.
The direction of the resultant displacement can be found using trigonometry. We can calculate the angle θ using the equation tan(θ) = opposite/adjacent. In this case, θ = tan^(-1)(opposite/adjacent) = tan^(-1)(-30/30) = -45°. However, since we established the north direction as positive y-axis, we need to convert this to a positive angle. So, the direction of the resultant displacement is 180° - 45° = 135° east of north.