Main Answer
The displacement of the bird in unit vector notation is (67.3i + 67.3j) km, and the average velocity for the trip is (31.7i + 31.7j) km/h, where i and j are unit vectors representing east and north directions, respectively.The option D is correct.
Step-by-step explanation
To calculate the displacement and average velocity of the bird, we need to know the distance and direction of its flight. The bird flies straight northeast for a distance of 95.0 km, which means that it moves 67.3 km in an easterly direction (i.e., due east) and 27.7 km in a northerly direction (i.e., due north).
Therefore, we can represent the displacement as a vector sum of these two components:displacement = (67.3i) km + (27.7j) km = (67.3i + 67.3j) km.To calculate the average velocity, we need to divide the total displacement by the total time taken by the bird:average velocity = displacement / time = (67.3i + 67.3j) km / 3.0 h = (31.7i + 31.7j) km/h.
This calculation shows that during its flight, the bird travels an average of 31.7 kilometers per hour in a direction that is 51 degrees east of north, as indicated by the vector sum of its eastward and northward components of motion.The option D is correct.