Question

A pedestrian walks 7.4 kilometers west and then 9.2 kilometers south. What is the direction of the pedestrian's resultant vector? Hint: Draw a vector diagram. Ө 0 = [ ? ]° Round your answer to the nearest hundredth

Answer 1

To determine the direction of the pedestrian's resultant vector, we can use vector addition and draw a vector diagram.

First, let's represent the westward displacement with a vector pointing to the left and labeled as 7.4 km. Then, we can represent the southward displacement with a vector pointing downward and labeled as 9.2 km.

To find the resultant vector, we need to connect the tail of the first vector (westward displacement) to the head of the second vector (southward displacement). The resultant vector represents the combined effect of both displacements.

Using the Pythagorean theorem, we can calculate the magnitude of the resultant vector:

Resultant magnitude = √(7.4^2 + 9.2^2) ≈ 11.7 km

Next, we can determine the direction of the resultant vector using trigonometry. The angle (Ө) between the resultant vector and the westward direction can be found using the inverse tangent:

Ө = arctan(9.2/7.4) ≈ 51.33°

Rounding to the nearest hundredth, the direction of the pedestrian's resultant vector is approximately 51.33° south of due west.