Final answer:
The resultant displacement of the pirate is approximately 12.39m. Option (A) is correct.
Step-by-step explanation:
To find the resultant displacement, we can break down the given displacements into their horizontal (east-west) and vertical (north-south) components.
First, the student walks 10m at an angle of 30 degrees north of east. We can determine the horizontal and vertical components using trigonometry:
Horizontal component = 10m * cos(30°) = 8.66m
Vertical component = 10m * sin(30°) = 5m
Next, the student turns west for a distance of 20m. Since this is a straight westward walk, the horizontal component is -20m and the vertical component is 0m.
To find the total displacement, we add the horizontal and vertical components:
Total horizontal displacement = 8.66m - 20m = -11.34m
Total vertical displacement = 5m + 0m = 5m
The resultant displacement is then given by:
Resultant displacement = √((-11.34m)^2 + 5m^2) = √(128.37m^2 + 25m^2) = √(153.37m^2) = 12.39m
Therefore, the resultant displacement of the pirate is approximately 12.39m.