The arshin is a unit of length formerly used in Russia up to about the end of WW

Question

The arshin is a unit of length formerly used in Russia up to about the end of WW1. A Russian soldier leaves his base and marches 560 arshins at an angle 25 degree north of east. He then turns and marches 210 arshins at an angle 10 degree west of north. There he spots an enemy patrol stopped 350 arshins due north of his position. See the figure below. 1 arshin = 2 .33 feet. Express the first displacement of the soldier rightarrow_s1 in unit vector notation Express the total displacement of the soldier rrightarrow_s-net in unit vector notation The soldier relays a message to his comrades at base camp informing them of the enemy patrol. If his comrades leave the base camp and march directly toward the enemy patrol, what will be their displacement when they reach the enemy? Express your answer as a magnitude in arshins and direction relative to east. Convert the magnitude of the displacement from C from arshins to meters.

Explanation / Answer

A)

rs1 = 560*cos25 i + 560*sin25 j = 507 i + 236.7 j

B)

rs2 = -210*sin10 i + 210*cos10 j = -36.5 i + 206.8 j

rsnet = rs1 + rs2 = 470.5 i + 443.5 j

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C)

r = rsnet + r3 = 470.5 i + 443.5 j + 350 j

r = 470.5i + 793.5 j

magnitude = sqrt(470.5^2+793.5^2) = 922.5 Arshins

direction = tan^-1(793.5/470.5) = 59.33

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D)

1 feet = 0.3048 m

r = 922.5 Arshins = 922.5*2.33*0.3048 = 655.14 m

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