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What is the resultant displacement of a pirate who walks for 10m at an angle of 30 degrees North of East and then turns west for a distance of 20m?"

a. Approximately 10.0m
b. Approximately 24.7m
c. Exactly 30.0m
d. Exactly 20.0m

1 Answer

3 votes

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.

User Thomas Schneiter
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