Final answer:
To find the total displacement, break down the given distances and directions into components. Find the x and y components for each leg of the walk. Add the x-components and the y-components separately to find the total displacement vector. Use the Pythagorean theorem to find the magnitude of the total displacement and the inverse tangent function to find the direction.
Step-by-step explanation:
To find the total displacement of your walk, we need to break down the given distances and directions into their respective components.
First, we can find the x-component of the displacement for the first leg of the walk by multiplying the distance by the cosine of the angle (12.5 m * cos(15°) = 11.95 m).
Next, we can find the y-component of the displacement for the first leg of the walk by multiplying the distance by the sine of the angle (12.5 m * sin(15°) = 3.15 m).
We repeat the same steps to find the x and y-components of the displacement for the second leg of the walk (27.5 m * cos(35°) = 22.62 m and 27.5 m * sin(35°) = 15.76 m).
Finally, we can add the x-components and the y-components separately to find the total displacement:
x-component: 11.95 m + 22.62 m = 34.57 m
y-component: 3.15 m + 15.76 m = 18.91 m
Using the Pythagorean theorem, we can find the magnitude of the total displacement:
magnitude = sqrt((34.57 m)^2 + (18.91 m)^2) = 39.7 m
To find the direction of the total displacement, we can use the inverse tangent function:
direction = atan(18.91 m / 34.57 m) = 29.9°
Therefore, the total displacement is 39.7 m at an angle of 29.9° south of west.