The atomic number of magnesium is 12. This means that its nucleus must contain
2 answers:
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(a) Since the lake has a circular shape, the distance they traveled is exactly 3/4 of a circumference. The radius of the lake is 2.51 km, and the circumference is given by 
, therefore the distance covered is
(b) We can consider the lake to be on a xy-plane with the origin of the axes being at the center of the lake. In this system of coordinates, the starting point of the motion is at the west side of the lake, so at coordinates (-2.51 km,0). The final point is after 3/4 of circumference, therefore at the north side, at coordinates (0, 2.51 km).
So we can calculate the magnitude of the displacement as
(c) Considering only the initial and final point of the motion, the couple moved 2.51 km north (on the x-axis) and 2.51 km east (on the y-axis). Therefore, we can calculate the angle of the displacement with respect to the east direction:
from which
(b) We can consider the lake to be on a xy-plane with the origin of the axes being at the center of the lake. In this system of coordinates, the starting point of the motion is at the west side of the lake, so at coordinates (-2.51 km,0). The final point is after 3/4 of circumference, therefore at the north side, at coordinates (0, 2.51 km).
So we can calculate the magnitude of the displacement as
(c) Considering only the initial and final point of the motion, the couple moved 2.51 km north (on the x-axis) and 2.51 km east (on the y-axis). Therefore, we can calculate the angle of the displacement with respect to the east direction:
from which