A dog searching for a bone walks 2.87 m south, then runs 22.5 m at an angle 30.5 north of east, and finally walks 5.91 m west. Find the direction of the dog's resultant displacement vector. Give your answer as an angle in degrees, with the angle measured counterclockwise from the line pointing straight East (North is 90, while South is -90).

This is a problem in adding three vectors. We will be glad to critique your work.

qwq

To find the direction of the dog's resultant displacement vector, we can use vector addition. Let's break down the dog's displacement into its horizontal (x) and vertical (y) components.

The dog walks 2.87 m south, so its displacement in the y-direction is -2.87 m.

The dog then runs 22.5 m at an angle 30.5 north of east. To find the x and y components, we can use trigonometry. The x-component is given by cos(30.5) * 22.5, and the y-component is sin(30.5) * 22.5.

x-component = cos(30.5°) * 22.5 = 19.42827 m

y-component = sin(30.5°) * 22.5 = 11.71876 m

Finally, the dog walks 5.91 m west, so its displacement in the x-direction is -5.91 m.

Now, we can add up the x-components and y-components separately to get the resultant displacement vector.

x-component: -5.91 m + 19.42827 m = 13.51827 m

y-component: -2.87 m + 11.71876 m = 8.84876 m

Using the x and y components, we can find the angle of the resultant displacement vector by using the inverse tangent function:

angle = arctan(y-component / x-component)

angle = arctan(8.84876 m / 13.51827 m)

angle ≈ 34.94°

The angle is measured counterclockwise from the line pointing straight East, so the direction of the dog's resultant displacement vector is approximately 34.94° counterclockwise from East.