Find the resultant of the following two vectors: i)40 units due east and ii)100 units 30° north of west.

A) 100 units 30° north of west
B) 68 units 17° north of west
C) 136 units 43° north of west
D) 68 units 47° north of west
E) 87 units 133° north of west

Question

Find the resultant of the following two vectors: i)40 units due east and ii)100 units 30° north of west.
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A) 100 units 30° north of west
B) 68 units 17° north of west
C) 136 units 43° north of west
D) 68 units 47° north of west
E) ​87 units 133° north of west

Quizplus · Accepted Answer

We can find the resultant of the two vectors using the method of vector addition.

First, we draw a diagram to represent the two vectors.

40 units due east can be represented by a vector pointing to the right (or along the positive x-axis).

100 units 30° north of west can be represented by a vector pointing in the direction between north and west, but closer to west. We can draw this vector by first drawing a vector pointing due west (or along the negative x-axis), and then rotating it 30° clockwise.

We can now add the two vectors by placing them head-to-tail, i.e., by putting the tail of the second vector at the head of the first vector.

The resulting vector is the vector that starts at the tail of the first vector and ends at the head of the second vector. We can measure the magnitude and direction of this vector using a ruler and a protractor.

The magnitude of the resultant vector is approximately 68 units, and its direction is approximately 47° north of west. Therefore, the correct answer is D) 68 units 47° north of west.

Find the Resultant of the Following Two Vectors: I)40 Units