Two tugboats are pulling a disabled speedboat into port with forces with 1240 lb
and 1480 lb. The angle between these forces 28.2°. Find the direction and magnitude of
the equilibrium.
please show all work/equations used
trigonometry help?
2016-05-05 2:56 pm
回答 (1)
2016-05-05 3:03 pm
Fix the x-axis in the direction of the larger force. Then the total force is
1480 i + 1240 i cos(28.2) + 1240 j sin(28.2)
= 2572.8 i + 585.96 j;
the magnitude of the resultant is
sqrt(2572.8^2 + 585.96^2) = about 2700 lb but use a calculator.
The angle between the resultant and the larger force is arctan(585.96/2572.8) = 12.8 degrees, so the direction of the equilibrating force, if that's what you're asking, is 167.2 degrees from the larger of the two tugboat forces described.
1480 i + 1240 i cos(28.2) + 1240 j sin(28.2)
= 2572.8 i + 585.96 j;
the magnitude of the resultant is
sqrt(2572.8^2 + 585.96^2) = about 2700 lb but use a calculator.
The angle between the resultant and the larger force is arctan(585.96/2572.8) = 12.8 degrees, so the direction of the equilibrating force, if that's what you're asking, is 167.2 degrees from the larger of the two tugboat forces described.
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