Question

The diagram shows two sets of vectors that result in a single vector.

Four vectors added using the tip to tail method. The first vector is labeled 100 meters and drawn east, the second vector is labeled 250 meters and drawn north, the third vector is labeled 200 meters and drawn east, the fourth vector is labeled 50 meters and drawn north. A last vector, the resultant, is drawn as a dashed arrow from the tail of the first to the tip of the last.

What are the first two steps for finding the magnitude of the resultant vector?

find the square of the first horizontal vector and the square root of the first vertical vector
find the square root of the first horizontal vector and the square root of the second horizontal vector
find the sum of the two horizontal vectors and the sum of the two vertical vectors
find the difference between the two horizontal vectors and the difference between the two vertical vectors

Answer 1

Answer: "find the sum of the two horizontal vectors and the sum of the two vertical vectors."

Explanation: Add horizontal components (100 + 200 = 300 m east) and vertical components (250 + 50 = 300 m north), then use the Pythagorean theorem: magnitude = sqrt(300^2 + 300^2) = 300√2 m.