Bradley is installing fencing on a farm. As he is installing the fencing, he moves 65.0 meters directly south, then turns, and goes 44.0 meters at an angle 25.0° east of south, where he finishes his work shift. What is his final displacement vector at the end of his shift??

a. 107m, 10.1°, east of south

b. 107m, 10.1° south of east

c. 121m, 14.1° south of east

d. 121m, 14.1° east of south

The correct option is;

a. 107 m, 10.1°, east of south

Explanation:

The given question can be answered using vectors as follows;

The initial displacement south by Bradley = 65.0 meters

In vector form, we have

The initial displacement south by Bradley = -65·j

The displacement 25.0° east of south = 44.0 meters

In vector form, we have

The displacement 25.0° east of south = 44 × sin(25°)·i - 44 × cos(25°)·j

In vector, form, we have;

The total displacement = The sum of the vectors of the two displacement

∴ The total displacement = -65·j + 44 × sin(25°)·i - 44 × cos(25°)·j

The total displacement = 44 × sin(25°)·i - (44 × cos(25°) + 65)·j

We use the i and j components to find the magnitude and the direction of the total displacement as follows;

The magnitude of the total displacement = √((44 × sin(25°))² + (44 × cos(25°) + 65)²) = 106.5132881 ≈ 107

The magnitude of the total displacement ≈ 107 m

The direction of the total displacement = arctan((44 × sin(25°))/((44 × cos(25°) + 65)) = 10.0542797419° ≈ 10.1° east of south