Grade 12 math: vectors as forces?

Two tugs are towing a ship. The smaller tug is 15 degrees off the port bow, and the larger tug is 20 degrees off the starboard bow. The larger tug pulls twice as hard as the smaller tug. In what direction will the ship move?

Question

Physics

Beasley

20 January, 15:01

Grade 12 math: vectors as forces?

Two tugs are towing a ship. The smaller tug is 15 degrees off the port bow, and the larger tug is 20 degrees off the starboard bow. The larger tug pulls twice as hard as the smaller tug. In what direction will the ship move?

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Answers (1)

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Ivan Velazquez · Answer 1

Larger tug force = 2*cos20 forward + 2*sin20 to the right (starboard)

Smaller tug force = 1*cos15 forward + 1*sin15 to the left (port)

Resultant force forward = 2*cos20 + 1*cos15 = 2.8453 (4dp)

Resultant force to right = 2*sin20 - 1*sin15 = 0.4252 (4dp)

Angle of resultant force = arctan (0.4252 / 2.8453) = arctan (0.1494) = 8.5 degrees

Grade 12 math: vectors as forces?Two tugs are towing a ship. The smaller tug is 15 degrees off the port bow, and the larger tug is 20 degrees off the starboard bow. The larger tug pulls twice as hard as the smaller tug. In what direction will the ship move?

Grade 12 math: vectors as forces?

Two tugs are towing a ship. The smaller tug is 15 degrees off the port bow, and the larger tug is 20 degrees off the starboard bow. The larger tug pulls twice as hard as the smaller tug. In what direction will the ship move?