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A pole is held vertically by attaching wires at a height of 13.4 m above the ground. The other end of each wire is anchored in the ground at a distnace of 9.54 m from the base of the pole. The pole makes a right angle with the ground. What is the length of each wire?b) 3 forces pull in different directions on an object at the origin. Once force has a magnitude of 100 newtons, and pulls at an angle 140 degrees with respect to the +x axis. The other two forces are 200 newtons at an angle of 70 degrees, and 160 newtons at an angle of 250 degress. Along what angle (in degress) could a single force of the appropriate magnitude point that would accomlish the same thing as the three factors acting together?

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sqdancefan

Answer:

  • 16.45 m
  • 121.7°

Step-by-step explanation:

a) The Pythagorean theorem is used to find the length of the hypotenuse of a right triangle from the the lengths of the legs:

  c² = a² + b²

  c = √(a² + b²) = √(13.4² +9.54²) ≈ 16.45 . . . meters

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b) Using an appropriate vector calculator, you can find the sum of the given forces to be ...

  100∠140° +200∠70° +160∠250° = 119.733∠121.704°

The forces have a resultant equivalent to a force at 121.7°.

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If you're calculating this by hand, you can add the components of the forces:

  a∠b = (a·cos(b), a·sin(b))

  100∠140° ≈ (-76.604, 64.279)

  200∠70° ≈ (68.404, 187.939)

  160∠250° ≈ (-54.723, -150.351)

(Values are shown rounded here. You never round intermediate calculations, but maintain full calculator precision until the final answer.) Then the sum of these forces is approximately ...

  resultant ≈ (-62.924, 101.866)

The (second quadrant) angle of this resultant is ...

  angle = arctan(101.866/-62.924) ≈ 121.7°

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