Question

A pedestrian moves 6.00 km east then 13.0 km north. Using the graphical method, find the magnitude and direction of the resultant displacement vector.

Answer 1

To find the magnitude and direction of a pedestrian's resultant displacement vector who moves 6.0 km east and then 13.0 km north, one must draw the displacement vectors graphically and use the Pythagorean theorem for magnitude and trigonometric functions for direction.

Step-by-step explanation:

Graphical Method to Find the Resultant Displacement

To use the graphical method to determine the pedestrian's resultant displacement, begin by drawing a vector representing the first displacement of 6.0 km east. This vector is drawn horizontally to the right. Next, from the endpoint of this vector, draw a second vector representing a 13.0 km north displacement. This vector is drawn vertically upward.

Now connect the start point of the first vector with the endpoint of the second vector to form the resultant displacement vector. The length of this diagonal represents the magnitude of the displacement, and the angle it makes with the horizontal (east direction) represents the direction of the displacement with respect to east.

The magnitude of the resultant displacement can be found using the Pythagorean theorem:
D = √((6.0 km)² + (13.0 km)²). The direction can be found by using the tangent function: θ = tan⁻¹(13.0 km / 6.0 km).

Answer 2

Resultant vector
r = (6^2 + 13^2)^0.5
r = (36 + 169)^0.5
r = 205^0.5
r = 14.13 km

Direction of the vector
tan theta = 13/6
tan theta = 2.17
theta = 65.22