Resultant displacement from 12m east to5m north to9m vertically upward
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To find the resultant displacement, you can use the method of vector addition.
1. Start by representing each displacement as a vector.
- The displacement of 12m east can be represented by a vector pointing to the right with a magnitude of 12m.
- The displacement of 5m north can be represented by a vector pointing upwards with a magnitude of 5m.
- The displacement of 9m vertically upward can be represented by a vector pointing upwards with a magnitude of 9m.
2. Draw these three vectors on a coordinate system, starting from the origin (0,0).
3. To add the vectors, place the tail of each vector at the head of the previous vector.
4. Connect the tail of the first vector to the head of the last vector, and this line represents the resultant vector.
5. Measure the magnitude of the resultant vector using a ruler or measuring tool.
In this case, you will have a triangle formed by the three vectors: the 12m east vector, the 5m north vector, and the 9m upwards vector.
To find the resultant displacement, measure the length of the line connecting the starting point (the tail of the first vector) to the ending point (the head of the last vector). This length represents the magnitude of the resultant displacement.
Using the Pythagorean theorem, we can calculate the magnitude of the resultant displacement:
Resultant displacement^2 = (12m)^2 + (5m)^2 + (9m)^2
Resultant displacement^2 = 144m^2 + 25m^2 + 81m^2
Resultant displacement^2 = 250m^2
Resultant displacement = sqrt(250m^2)
Resultant displacement ≈ 15.81m
Therefore, the resultant displacement from 12m east, 5m north, and 9m vertically upward is approximately 15.81m.