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A bird flies straight northeast a distance of 95.0 km for 3.0 h. With the x-axis due east and the y-axis due north, what is the displacement in unit vector notation for the bird? What is the average velocity for the trip?

a) Option a: Displacement = (67.3ˆi + 67.3ˆj) km, Average velocity = (31.7ˆi + 31.7ˆj) km/h
b) Option a: Displacement = (95.0ˆi + 0ˆj) km, Average velocity = (31.7ˆi + 0ˆj) km/h
c) Option a: Displacement = (0ˆi + 95.0ˆj) km, Average velocity = (0ˆi + 31.7ˆj) km/h
d) Option a: Displacement = (67.3ˆi + 0ˆj) km, Average velocity = (31.7ˆi + 0ˆj) km/h

User Dinre
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1 Answer

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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.

User Palasaty
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