
Concept explainers
To Determine:
- The components of the velocity vector in the north and west directions.
- The distance in far north and far west covered by the plane after 1.75 h.
Solution:
- The component of the velocity vector in the northerly direction is 625 km/h and the component of the velocity vector in the westerly direction is -553 km/h.
- After 1.75 h the airplane travels 1094 km inthe north and 968 km inthe west.
Section 1:
c. To Determine:The components of the velocity vector in the north and west directions.
Solution:The component of the velocity vector in the northerly direction is 625 km/h and the component of the velocity vector in the westerly direction is -553 km/h.
Explanation:
Given: The magnitude of the velocity vector
Formula used:
The component in the westerly direction is equivalent to x-component, so:
Similarly, the component in the northerly direction is equivalent to y-component, therefore:
Calculation:
Inserting the magnitude of velocity vector and direction into equations (1) and (2) we obtain:
And
Therefore, the component of the velocity vector in the northerly direction is 625km/h and the component of the velocity vector in the westerly direction is -553 km/h.
Section 2:
- To Determine:The distance in far north and far west covered by the plane after 1.75 h.
Solution:After 1.75 h the airplane travels 1094 km at the north and 968 km at the west
Explanation:
Given:
The component of the velocity vector in the northerly direction is 625 km/h and the component of the velocity vector in the westerly direction is -553 km/h. The timet is 1.75 h.
Formula used:
Assuming the airplane travels at a constant speed, the distance x traveled in each direction can be obtained using:
Where:
- v is the component of vthe elocity vector
- t is the time elapsed
Calculation:
The distance at the north
Now, the distance at the west
Therefore, after 1.75 h the airplane travels 1094 km at the north and 968 km at the west.
Conclusion:
The component of the velocity vector in the northerly direction is 625 km/h, and the component of the velocity vector in the westerly direction is -553 km/h. After 1.75 h the airplane travels 1094 km at the north and 968 km at the west.ss
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