A map suggests that Atlanta is 730 miles in a direction 5.00 degrees� north of east from Dallas....

Question:

A map suggests that Atlanta is {eq}730\: miles {/eq} in a direction {eq}5.00^{\circ} {/eq} north of east from Dallas. The same map shows that Chicago is {eq}560\: miles {/eq} in a direction {eq}21.0^{\circ} {/eq} west of north from Atlanta. The figure below shows the location of these three cities. Modeling the Earth as flat, use this information to find the displacement from Dallas to Chicago.

magnitude

direction {eq}\:\:\:\:\:\:\:^{\circ} {/eq} north of east of Dallas

Vector Addition:

A vector is a mathematical object that has a magnitude and a direction. We can think of them visually as arrows pointing in space, where the length of the arrow represents the magnitude of the vector.

Visually, adding two vectors is equivalent to placing the tail of one vector on the head of another, then tracing out the straight line from the first tail to the second head. However, it is easier to compute the sum of two vectors if we instead interpret them as the x- and y-coordinates of the arrow's head when its tail is placed at the origin. The components of the sum of two vectors are the sum of the x-components and the sum of the y-components, respectively.

{eq}V_a + V_b = \langle a_x, a_y \rangle + \langle b_x, b_y \rangle = \langle a_x + b_x, a_y + b_y \rangle {/eq}

Answer and Explanation: 1