# determine the total distance traveled and the displacement made. A. 5.0 km 15 degrees east of north B. 5.0 km 20 degrees east of south C. 5.0 km east D. 5.0 km 30 degrees south of west E....

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### 1 Answer

Beginning the journey at the origin, and considering the directions and 5 kM distance travelled in each direction, the co-ordinates of points A through J can be worked out by adding/subtracting sine and cosine functions of the subtended angles, multiplied by 5 in each position.

These coordinates are as follows:

Point x-coordinate y-coordinate --------- ---------------- -------------------

A 1.2941 4.8296

B 3.0042 0.1312

C 8.0042 0.1312

D 3.6741 -2.3688

E 5.3842 -7.0673

F 1.5539 -3.8534

G -1.6600 -7.6836

H -0.3659 -2.8540

I -4.6960 -0.3540

J 0.3040 -0.3540

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Finally, the overall displacement (i.e. distance between origin, O and final point, J) is obtained from the two-point distance formula:

OJ`= [sqrt((0.3040-0)^2+(-0.3540-0)^2)] =0.467` kM

Distance travelled = 5*10=50 kM.

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