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) these three displacements:
72.4 m, 32.0° east of north;
57.3 m, 36.0° south of west;
17.8 m straight south.
The three displacements lead to the point where the keys to a new Porsche are buried. The finder gets the Porsche. Three of the four contestants start measuring immediately, but the winner first calculates where to go. What does he calculate?
Part A - Practice Problem:
In a second contest, the three displacements given are 70.2 m, 54° west of north; 15.3 m straight north; and 90.1 m, 40° south of east. What magnitude does the winner calculate for the displacement to find the keys to the Porsche?
Express your answer in meters.
Part B - Practice Problem:
What direction does the winner calculate for the displacement to find the keys to the Porsche?
Express your answer in degrees.