2. A traveling salesman takes a road trip that consists of four consecutive disp
ID: 1871993 • Letter: 2
Question
2. A traveling salesman takes a road trip that consists of four consecutive displacements: A= (16,-12) km B (14, 18) km C (0,-21) km D = (-25,-16) km a. (I pt.) Find his total displacement R from his initial starting point. Write R below in any standard coordinate notation. You do NOT need to show your work. For significant figures, assume that the above values are exact. Be sure to include units on your final answer! R= b. (4 pts) Find the magnitude and direction (angle) for the resultant vector in part (a). (Use the standard "trigonometric" definition for angle: let the direction of =0° be along the positive r-axis, and let e increase counterclockwise.) Show your work completely. Express your final magnitude to 3 significant figures, and express your final direction to the nearest O.1.Explanation / Answer
(A) R = A + B + C + D
= (16 + 14 + 0 + (-25) , -12 + 18 - 21 - 16 )km
R = (5 , -31)km
(B) Mgnitude = sqrt(5^2 + (-31)^2)
=31.4 km
direction angle = 360 - tan^-1(31/5)
= 279 deg
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