A traveling salesman takes a road trip that consists of four consecutive displac

Question

A traveling salesman takes a road trip that consists of four consecutive displacements:

A=(-28,15) km B=(13,22) km C=(0,-42) km D=(-14,-27) km

A) Find his total displacement R form his initial starting point. Write this sum below in any standard coordinate notation. Be sure to include units on your final answer.

B) Find the magnitude and direction (angle) for the resultant vector in part A. (Use the standard "trigonometric" definition for angle: let the direction of theta equal zero be along the positive x=axis, and let theta increase counterclockwise.) Express your final magnitude to 3 significant figures, and express your final direction to the nearest 0.1 degree.

Explanation / Answer

part a)

initial point is A=r1

final point is D=r2

displacement=r2-r1

now r1=(282+152)1/2

r2=(142+272)1/2

r=|r2-r1|

part b)

let angle between r1 and r2 is theta

r=r1r2cos(theta)

theta=cos inverse(r/r1r2)

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