Answer:
The correct option is;
a. 107 m, 10.1°, east of south
Step-by-step 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