Question Detail

We need to add the vectors. East is +x, north is +y. First leg: D1 = 620 km, 0° => components (620, 0). Second leg: southeast 45° means 45° below +x axis, so components: (440 cos45°, -440 sin45°) = (440×0.7071, -440×0.7071) = (311.1, -311.1). Third leg: 53° south of west means from west (180°) go 53° toward south, so angle = 180° + 53°? Actually south of west means starting from west and turning south, so the direction is 180° + 53°? No, south of west means the vector points west and then south, so the angle from positive x-axis is 180° - 53°? Let's be careful: If it's 53° south of west, that means the direction is 53° toward the south from the west direction. So from the negative x-axis, rotate 53° toward negative y. So the angle from positive x-axis is 180° + ( -53°)? Actually, standard: 0° east, 90° north, 180° west, 270° south. South of west means between west and south, so angles between 180° and 270°. Specifically, 53° south of west means from west (180°) go 53° toward south, so the angle is 180° + 53° = 233° from positive x-axis. But that would be 53° past west toward south. Alternatively, we can think: components: west component = 550 cos53°, south component = 550 sin53°. cos53°≈0.6, sin53°≈0.8. So x-component = -550 cos53° = -550×0.6 = -330 km, y-component = -550 sin53° = -550×0.8 = -440 km. Now sum components: x_total = 620 + 311.1 - 330 = 601.1 km. y_total = 0 - 311.1 - 440 = -751.1 km. Magnitude = √(601.1² + 751.1²) = √(361321 + 564151) = √925472 ≈ 962 km. Angle below x-axis: tanθ = 751.1/601.1 = 1.25, θ = 51.3° below positive x-axis. So approximately 960.5 km at 51° below the x-axis. Option A matches.