The first displacement is 8 m,and the second displacement is 4 m.They cannot add together to give a total displacement of:

A) 3 m.
B) 4 m.
C) 5 m.
D) 6 m.
E) 7 m.

Question

The first displacement is 8 m,and the second displacement is 4 m.They cannot add together to give a total displacement of:
​
A) 3 m.
B) 4 m.
C) 5 m.
D) 6 m.
E) ​7 m.

Quizplus · Accepted Answer

Displacements are vector quantities and they have both magnitude and direction. The total displacement is the vector sum of individual displacements. If the two given displacements are in opposite directions, then their vector sum would be the difference of their magnitudes (8 m - 4 m = 4 m) in the direction of the larger displacement. However, if they are in the same direction, then their vector sum would be the sum of their magnitudes (8 m + 4 m = 12 m) in the same direction. In this case, since none of the answer choices matches the result of summing or subtracting the given displacements, we can conclude that they are not in the same or opposite directions, but rather they are perpendicular to each other. Therefore, using the Pythagorean theorem, we can find the magnitude of the total displacement as:
total displacement = sqrt((8 m)^2 + (4 m)^2) = sqrt(80) m approx. 8.9 m
This value is not included in the answer choices. Therefore, the correct answer is A) 3 m which is just a distractor that results from adding or subtracting the given displacements in the wrong way.

The First Displacement Is 8 M,and the Second Displacement Is