A bird watcher meanders through the woods, walking 0.45 km due east, 0.80 km due south, and 2.05 km in a direction 43.0° north of west. The time required for this trip is 2.50 h.

(a) Determine the magnitude and direction (relative to due west) of the bird watcher's displacement. Use kilometers and hours for distance and time, respectively. magnitude 1 km
direction 2 ° north of west

(b) Determine the magnitude and direction (relative to due west) of the bird watcher's average velocity. magnitude 3 km/hr
direction 4 ° north of west

To determine the magnitude and direction of the bird watcher's displacement, we need to calculate the total distance traveled in the east-west and north-south directions.

In the east-west direction:
Distance = 0.45 km (east) - 2.05 km (west)
Distance = -1.6 km

In the north-south direction:
Distance = -0.8 km (south) + 2.05 km * sin(43°) (north)
Distance = 0.88 km

To calculate the magnitude of the displacement, we can use the Pythagorean theorem:
Magnitude = sqrt((-1.6 km)^2 + (0.88 km)^2)
Magnitude ≈ 1.83 km

To determine the direction relative to due west, we can use trigonometry:
Direction = atan(0.88 km / 1.6 km)
Direction ≈ 28.2° north of west

Therefore, the magnitude of the bird watcher's displacement is approximately 1.83 km, and the direction relative to due west is approximately 28.2° north of west.

To determine the magnitude and direction of the bird watcher's average velocity, we need to divide the displacement by the time taken.

Magnitude = 1.83 km / 2.5 h
Magnitude ≈ 0.73 km/h

To find the direction, we need to find the tangent of the angle between the displacement and the time taken.
Direction = atan((0.88 km) / (1.6 km * 2.5 h))
Direction ≈ 16.92° north of west

Therefore, the magnitude of the bird watcher's average velocity is approximately 0.73 km/h, and the direction relative to due west is approximately 16.92° north of west.