Consider four finalists in a treasure hunt who are brought to the center of a la
ID: 1406418 • Letter: C
Question
Consider four finalists in a treasure hunt who are brought to the center of a large, flat field. Each is given a meterstick, a compass, a calculator, a shovel, and (in a different order for each contestant)
1. In a second contest, the three displacements given are 60.4 m , 54 ? west of north; 15 m straight north; and 83.5 m , 42 ? south of east. What magnitude does the winner calculate for the displacement to find the keys to the Porsche? Express your answer in meters to three significant figures.
2. ?What direction does the winner calculate for the displacement to find the keys to the Porsche?
y (north) 36.0° 57.3 m A 72.4 m 17.8 mC 32.0 -x (east)Explanation / Answer
r = r1 + r2 + r3
r1 = 60.4m 54 degrees west of north
r1 = 60.4 ( -sin54i + cos54j)
r2 = 15j
r3 = 83.5 ( cos42i - sin42j)
r = 13.19i - 5.30j
magnitude = sqrt(13.19^2 + 5.30^2) = 14.22 m
2. direction = tan^-1 ( 5.30 / 13.19) south of east
= 21.90 degrees south of east
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